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  • Realizing Omega-regular Hyperproperties
    arXiv.cs.LO Pub Date : 2021-01-18
    Bernd Finkbeiner; Christopher Hahn; Jana Hofmann; Leander Tentrup

    We studied the hyperlogic HyperQPTL, which combines the concepts of trace relations and $\omega$-regularity. We showed that HyperQPTL is very expressive, it can express properties like promptness, bounded waiting for a grant, epistemic properties, and, in particular, any $\omega$-regular property. Those properties are not expressible in previously studied hyperlogics like HyperLTL. At the same time

    更新日期:2021-01-19
  • Efficient Monitoring of Hyperproperties using Prefix Trees
    arXiv.cs.LO Pub Date : 2021-01-18
    Bernd Finkbeiner; Christopher Hahn; Marvin Stenger; Leander Tentrup

    Hyperproperties, such as non-interference and observational determinism, relate multiple computation traces with each other and are thus not monitorable by tools that consider computations in isolation. We present the monitoring approach implemented in the latest version of RVHyper, a runtime verification tool for hyperproperties. The input to the tool are specifications given in the temporal logic

    更新日期:2021-01-19
  • Reversible Computation in Petri Nets
    arXiv.cs.LO Pub Date : 2021-01-04
    Kyriaki Psara

    Reversible computation is an unconventional form of computing that extends the standard forward-only mode of computation with the ability to execute a sequence of operations in reverse at any point during computation. As such, in this thesis we propose a reversible approach to Petri nets by introducing machinery and associated operational semantics to tackle the challenges of the main forms of reversibility

    更新日期:2021-01-19
  • Counterexample-Guided Prophecy for Model Checking Modulo the Theory of Arrays
    arXiv.cs.LO Pub Date : 2021-01-18
    Makai Mann; Ahmed Irfan; Alberto Griggio; Oded Padon; Clark Barrett

    We develop a framework for model checking infinite-state systems by automatically augmenting them with auxiliary variables, enabling quantifier-free induction proofs for systems that would otherwise require quantified invariants. We combine this mechanism with a counterexample-guided abstraction refinement scheme for the theory of arrays. Our framework can thus, in many cases, reduce inductive reasoning

    更新日期:2021-01-19
  • dtControl 2.0: Explainable Strategy Representation via Decision Tree Learning Steered by Experts
    arXiv.cs.LO Pub Date : 2021-01-15
    Pranav Ashok; Mathias Jackermeier; Jan Křetínský; Christoph Weinhuber; Maximilian Weininger; Mayank Yadav

    Recent advances have shown how decision trees are apt data structures for concisely representing strategies (or controllers) satisfying various objectives. Moreover, they also make the strategy more explainable. The recent tool dtControl had provided pipelines with tools supporting strategy synthesis for hybrid systems, such as SCOTS and Uppaal Stratego. We present dtControl 2.0, a new version with

    更新日期:2021-01-19
  • Computability of Data-Word Transductions over Different Data Domains
    arXiv.cs.LO Pub Date : 2021-01-18
    Léo Exibard; Emmanuel Filiot; Nathan Lhote; Pierre-Alain Reynier

    In this paper, we investigate the problem of synthesizing computable functions of infinite words over an infinite alphabet (data $\omega$-words). The notion of computability is defined through Turing machines with infinite inputs which can produce the corresponding infinite outputs in the limit. We use non-deterministic transducers equipped with registers, an extension of register automata with outputs

    更新日期:2021-01-19
  • Simple Stochastic Games with Almost-Sure Energy-Parity Objectives are in NP and coNP
    arXiv.cs.LO Pub Date : 2021-01-18
    Richard Mayr; Sven Schewe; Patrick Totzke; Dominik Wojtczak

    We study stochastic games with energy-parity objectives, which combine quantitative rewards with a qualitative $\omega$-regular condition: The maximizer aims to avoid running out of energy while simultaneously satisfying a parity condition. We show that the corresponding almost-sure problem, i.e., checking whether there exists a maximizer strategy that achieves the energy-parity objective with probability

    更新日期:2021-01-19
  • Higher Order Automatic Differentiation of Higher Order Functions
    arXiv.cs.LO Pub Date : 2021-01-17
    Mathieu Huot; Sam Staton; Matthijs Vákár

    We present semantic correctness proofs of automatic differentiation (AD). We consider a forward-mode AD method on a higher order language with algebraic data types, and we characterise it as the unique structure preserving macro given a choice of derivatives for basic operations. We describe a rich semantics for differentiable programming, based on diffeological spaces. We show that it interprets our

    更新日期:2021-01-19
  • HySTER: A Hybrid Spatio-Temporal Event Reasoner
    arXiv.cs.LO Pub Date : 2021-01-17
    Theophile Sautory; Nuri Cingillioglu; Alessandra Russo

    The task of Video Question Answering (VideoQA) consists in answering natural language questions about a video and serves as a proxy to evaluate the performance of a model in scene sequence understanding. Most methods designed for VideoQA up-to-date are end-to-end deep learning architectures which struggle at complex temporal and causal reasoning and provide limited transparency in reasoning steps.

    更新日期:2021-01-19
  • Towards Approximate Query Enumeration with Sublinear Preprocessing Time
    arXiv.cs.LO Pub Date : 2021-01-15
    Isolde Adler; Polly Fahey

    This paper aims at providing extremely efficient algorithms for approximate query enumeration on sparse databases, that come with performance and accuracy guarantees. We introduce a new model for approximate query enumeration on classes of relational databases of bounded degree. We first prove that on databases of bounded degree any local first-order definable query can be enumerated approximately

    更新日期:2021-01-18
  • Switched Systems as Hybrid Programs
    arXiv.cs.LO Pub Date : 2021-01-15
    Yong Kiam Tan; André Platzer

    Real world systems of interest often feature interactions between discrete and continuous dynamics. Various hybrid system formalisms have been used to model and analyse this combination of dynamics, ranging from mathematical descriptions, e.g., using impulsive differential equations and switching, to automata-theoretic and language-based approaches. This paper bridges two such formalisms by showing

    更新日期:2021-01-18
  • An Abstract Contract Theory for Programs with Procedures
    arXiv.cs.LO Pub Date : 2021-01-15
    Christian LidströmKTH Royal Institute of Technology, Stockholm, Sweden; Dilian GurovKTH Royal Institute of Technology, Stockholm, Sweden

    When developing complex software and systems, contracts provide a means for controlling the complexity by dividing the responsibilities among the components of the system in a hierarchical fashion. In specific application areas, dedicated contract theories formalise the notion of contract and the operations on contracts in a manner that supports best the development of systems in that area. At the

    更新日期:2021-01-18
  • LIME: Learning Inductive Bias for Primitives of Mathematical Reasoning
    arXiv.cs.LO Pub Date : 2021-01-15
    Yuhuai Wu; Markus Rabe; Wenda Li; Jimmy Ba; Roger Grosse; Christian Szegedy

    While designing inductive bias in neural architectures has been widely studied, we hypothesize that transformer networks are flexible enough to learn inductive bias from suitable generic tasks. Here, we replace architecture engineering by encoding inductive bias in the form of datasets. Inspired by Peirce's view that deduction, induction, and abduction form an irreducible set of reasoning primitives

    更新日期:2021-01-18
  • Deadlock in packet switching networks
    arXiv.cs.LO Pub Date : 2021-01-15
    Anna Stramaglia; Jeroen J. A. Keiren; Hans Zantema

    A deadlock in a packet switching network is a state in which one or more messages have not yet reached their target, yet cannot progress any further. We formalize three different notions of deadlock in the context of packet switching networks, to which we refer as global, local and weak deadlock. We establish the precise relations between these notions, and prove they characterize different sets of

    更新日期:2021-01-18
  • A Strong Bisimulation for Control Operators by Means of Multiplicative and Exponential Reduction
    arXiv.cs.LO Pub Date : 2021-01-14
    Eduardo Bonelli; Delia Kesner; Andrés Viso

    The purpose of this paper is to identify programs with control operators whose reduction semantics are in exact correspondence. This is achieved by introducing a relation $\simeq$, defined over a revised presentation of Parigot's $\lambda\mu$-calculus we dub $\Lambda M$. Our result builds on three main ingredients which guide our semantical development: (1) factorization of Parigot's $\lambda\mu$-reduction

    更新日期:2021-01-15
  • Lebesgue integration. Detailed proofs to be formalized in Coq
    arXiv.cs.LO Pub Date : 2021-01-14
    François ClémentSERENA, CERMICS; Vincent MartinLMAC

    To obtain the highest confidence on the correction of numerical simulation programs implementing the finite element method, one has to formalize the mathematical notions and results that allow to establish the soundness of the method. Sobolev spaces are the correct framework in which most partial derivative equations may be stated and solved. These functional spaces are built on integration and measure

    更新日期:2021-01-15
  • Analysis of E-commerce Ranking Signals via Signal Temporal Logic
    arXiv.cs.LO Pub Date : 2021-01-14
    Tommaso DreossiAmazon Search; Giorgio BallardinAmazon Search; Parth GuptaAmazon Search; Jan BakusAmazon Search; Yu-Hsiang LinAmazon Search; Vamsi SalakaAmazon Search

    The timed position of documents retrieved by learning to rank models can be seen as signals. Signals carry useful information such as drop or rise of documents over time or user behaviors. In this work, we propose to use the logic formalism called Signal Temporal Logic (STL) to characterize document behaviors in ranking accordingly to the specified formulas. Our analysis shows that interesting document

    更新日期:2021-01-15
  • Enclosing the Sliding Surfaces of a Controlled Swing
    arXiv.cs.LO Pub Date : 2021-01-14
    Luc JaulinRobex, Lab-STICC; Benoît DesrochersDGA-TN

    When implementing a non-continuous controller for a cyber-physical system, it may happen that the evolution of the closed-loop system is not anymore piecewise differentiable along the trajectory, mainly due to conditional statements inside the controller. This may lead to some unwanted chattering effects than may damage the system. This behavior is difficult to observe even in simulation. In this paper

    更新日期:2021-01-15
  • Irrationality and Transcendence Criteria for Infinite Series in Isabelle/HOL
    arXiv.cs.LO Pub Date : 2021-01-08
    Angeliki Koutsoukou-Argyraki; Wenda Li; Lawrence C. Paulson

    We give an overview of our formalizations in the proof assistant Isabelle/HOL of certain irrationality and transcendence criteria for infinite series from three different research papers: by Erd\H{o}s and Straus (1974), Han\v{c}l (2002), and Han\v{c}l and Rucki (2005). Our formalizations in Isabelle/HOL can be found on the Archive of Formal Proofs. Here we describe selected aspects of the formalization

    更新日期:2021-01-14
  • Proceedings 6th International Workshop on Symbolic-Numeric methods for Reasoning about CPS and IoT
    arXiv.cs.LO Pub Date : 2021-01-01
    Thao DangVerimag/CNRS, France; Stefan RatschanInstitute of Computer Science, Czech Academy of Sciences

    The proceedings of the 6th International Workshop on Symbolic-Numeric Methods for Reasoning about CPS and IoT (SNR 2020) contains papers underlying talks presented at the workshop. SNR focuses on the combination of symbolic and numeric methods for reasoning about Cyber-Physical Systems and the Internet of Things to facilitate model identification, specification, verification, and control synthesis

    更新日期:2021-01-14
  • Secure Process Algebra
    arXiv.cs.LO Pub Date : 2021-01-13
    Yong Wang

    Based on our previous work on truly concurrent process algebras APTC, we use it to verify the security protocols. This work (called Secure APTC, abbreviated SAPTC) have the following advantages in verifying security protocols: (1) It has a firmly theoretic foundations, including equational logics, structured operational semantics, and axiomatizations between them; (2) It has rich expressive powers

    更新日期:2021-01-14
  • Proposal for Adding Useful Features to Petri-Net Model Checkers
    arXiv.cs.LO Pub Date : 2021-01-13
    Hubert GaravelCONVECS

    Solutions proposed for the longstanding problem of automatic decomposition of Petri nets into concurrent processes, as well as methods developed in Grenoble for the automatic conversion of safe Petri nets to NUPNs (Nested-Unit Petri Nets), require certain properties to be computed on Petri nets. We notice that, although these properties are theoretically interesting and practically useful, they are

    更新日期:2021-01-14
  • An Algebraic Method to Fidelity-based Model Checking over Quantum Markov Chains
    arXiv.cs.LO Pub Date : 2021-01-13
    Ming XuShanghai Key Lab of Trustworthy Computing, East China Normal University, Shanghai, China; Jianling FuShanghai Key Lab of Trustworthy Computing, East China Normal University, Shanghai, China; Jingyi MeiShanghai Key Lab of Trustworthy Computing, East China Normal University, Shanghai, China; Yuxin DengShanghai Key Lab of Trustworthy Computing, East China Normal University, Shanghai, China

    Fidelity is one of the most widely used quantities in quantum information that measure the distance of quantum states through a noisy channel. In this paper, we introduce a quantum analogy of computation tree logic (CTL) called QCTL, which concerns fidelity instead of probability in probabilistic CTL, over quantum Markov chains (QMCs). Noisy channels are modelled by super-operators, which are specified

    更新日期:2021-01-14
  • Parametricity for Nested Types and GADTs
    arXiv.cs.LO Pub Date : 2021-01-13
    Patricia Johann; Enrico Ghiorzi; Daniel Jeffries

    This paper considers parametricity and its consequent free theorems for nested data types. Rather than representing nested types via their Church encodings in a higher-kinded or dependently typed extension of System F, we adopt a functional programming perspective and design a Hindley-Milner-style calculus with primitives for constructing nested types directly as fixpoints. Our calculus can express

    更新日期:2021-01-14
  • Register Automata with Extrema Constraints, and an Application to Two-Variable Logic
    arXiv.cs.LO Pub Date : 2021-01-11
    Szymon Toruńczyk; Thomas Zeume

    We introduce a model of register automata over infinite trees with extrema constraints. Such an automaton can store elements of a linearly ordered domain in its registers, and can compare those values to the suprema and infima of register values in subtrees. We show that the emptiness problem for these automata is decidable. As an application, we prove decidability of the countable satisfiability problem

    更新日期:2021-01-12
  • Implementation of Two Layers Type Theory in Dedukti and Application to Cubical Type Theory
    arXiv.cs.LO Pub Date : 2021-01-11
    Bruno BarrasInria, Université Paris-Saclay, ENS Paris-Saclay, CNRS, LSV, Gif-sur-Yvette, France; Valentin MaestracciUniversité Paris-Saclay, ENS Paris-Saclay, CNRS, LSV, Gif-sur-Yvette, France

    In this paper, we make a substantial step towards an encoding of Cubical Type Theory (CTT) in the Dedukti logical framework. Type-checking CTT expressions features a decision procedure in a de Morgan algebra that so far could not be expressed by the rewrite rules of Dedukti. As an alternative, 2 Layer Type Theories are variants of Martin-L\"of Type Theory where all or part of the definitional equality

    更新日期:2021-01-12
  • Deductive Systems and Coherence for Skew Prounital Closed Categories
    arXiv.cs.LO Pub Date : 2021-01-11
    Tarmo Uustalu; Niccolò Veltri; Noam Zeilberger

    In this paper, we develop the proof theory of skew prounital closed categories. These are variants of the skew closed categories of Street where the unit is not represented. Skew closed categories in turn are a weakening of the closed categories of Eilenberg and Kelly where no structural law is required to be invertible. The presence of a monoidal structure in these categories is not required. We construct

    更新日期:2021-01-12
  • Object-Level Reasoning with Logics Encoded in HOL Light
    arXiv.cs.LO Pub Date : 2021-01-11
    Petros PapapanagiotouUniversity of Edinburgh; Jacques FleuriotUniversity of Edinburgh

    We present a generic framework that facilitates object level reasoning with logics that are encoded within the Higher Order Logic theorem proving environment of HOL Light. This involves proving statements in any logic using intuitive forward and backward chaining in a sequent calculus style. It is made possible by automated machinery that take care of the necessary structural reasoning and term matching

    更新日期:2021-01-12
  • Mechanisation of Model-theoretic Conservative Extension for HOL with Ad-hoc Overloading
    arXiv.cs.LO Pub Date : 2021-01-11
    Arve Gengelbach; Johannes Åman Pohjola; Tjark Weber

    Definitions of new symbols merely abbreviate expressions in logical frameworks, and no new facts (regarding previously defined symbols) should hold because of a new definition. In Isabelle/HOL, definable symbols are types and constants. The latter may be ad-hoc overloaded, i.e. have different definitions for non-overlapping types. We prove that symbols that are independent of a new definition may keep

    更新日期:2021-01-12
  • Tietze Equivalences as Weak Equivalences
    arXiv.cs.LO Pub Date : 2021-01-10
    Simon Henry; Samuel Mimram

    A given monoid usually admits many presentations by generators and relations and the notion of Tietze equivalence characterizes when two presentations describe the same monoid: it is the case when one can transform one presentation into the other using the two families of so-called Tietze transformations. The goal of this article is to provide an abstract and geometrical understanding of this well-known

    更新日期:2021-01-12
  • Polymorphic System I
    arXiv.cs.LO Pub Date : 2021-01-08
    Cristian F. Sottile; Alejandro Díaz-Caro; Pablo E. Martínez López

    System I is a simply-typed lambda calculus with pairs, extended with an equational theory obtained from considering the type isomorphisms as equalities. In this work we propose an extension of System I to polymorphic types, adding the corresponding isomorphisms. We provide non-standard proofs of subject reduction and strong normalisation, extending those of System I.

    更新日期:2021-01-12
  • A Rewriting Logic Approach to Specification, Proof-search, and Meta-proofs in Sequent Systems
    arXiv.cs.LO Pub Date : 2021-01-08
    Carlos Olarte; Elaine Pimentel; Camilo Rocha

    This paper develops an algorithmic-based approach for proving inductive properties of propositional sequent systems such as admissibility, invertibility, cut-elimination, and identity expansion. Although undecidable in general, these structural properties are crucial in proof theory because they can reduce the proof-search effort and further be used as scaffolding for obtaining other meta-results such

    更新日期:2021-01-11
  • Quotients, inductive types, and quotient inductive types
    arXiv.cs.LO Pub Date : 2021-01-08
    Marcelo P. Fiore; Andrew M. Pitts; S. C. Steenkamp

    This paper introduces an expressive class of indexed quotient-inductive types, called QWI types, within the framework of constructive type theory. They are initial algebras for indexed families of equational theories with possibly infinitary operators and equations. We prove that QWI types can be derived from quotient types and inductive types in the type theory of toposes with natural number object

    更新日期:2021-01-11
  • Proceedings Fifteenth Workshop on Logical Frameworks and Meta-Languages: Theory and Practice
    arXiv.cs.LO Pub Date : 2021-01-08
    Claudio Sacerdoti CoenUniversity of Bologna; Alwen TiuThe Australian National University

    This volume contains a selection of papers presented at LFMTP 2020, the 15th International Workshop on Logical Frameworks and Meta-Languages: Theory and Practice (LFMTP), held the 29-30th of June, 2019, using the Zoom video conferencing tool due to COVID restrictions. Officially the workshop was held in Paris, France, and it was affiliated with IJCAR 2020, FSCD 2020 and many other satellite events

    更新日期:2021-01-11
  • Theorem Proving and Algebra
    arXiv.cs.LO Pub Date : 2021-01-07
    Joseph A. Goguen

    This book can be seen either as a text on theorem proving that uses techniques from general algebra, or else as a text on general algebra illustrated and made concrete by practical exercises in theorem proving. The book considers several different logical systems, including first-order logic, Horn clause logic, equational logic, and first-order logic with equality. Similarly, several different proof

    更新日期:2021-01-08
  • On the Convergence of Tsetlin Machines for the XOR Operator
    arXiv.cs.LO Pub Date : 2021-01-07
    Lei Jiao; Xuan Zhang; Ole-Christoffer Granmo; K. Darshana Abeyrathna

    The Tsetlin Machine (TM) is a novel machine learning algorithm with several distinct properties, including transparent inference and learning using hardware-near building blocks. Although numerous papers explore the TM empirically, many of its properties have not yet been analyzed mathematically. In this article, we analyze the convergence of the TM when input is non-linearly related to output by the

    更新日期:2021-01-08
  • Merging with unknown reliability
    arXiv.cs.LO Pub Date : 2021-01-07
    Paolo Liberatore

    Merging beliefs depends on the relative reliability of their sources. When unknown, assuming equal reliability is unwarranted. The solution proposed in this article is that every reliability profile is possible, and only what holds according to all is accepted. Alternatively, one source is completely reliable, but which one is unknown. These two cases motivate two existing forms of merging: maxcons-based

    更新日期:2021-01-08
  • Parallel Hyperedge Replacement Grammars
    arXiv.cs.LO Pub Date : 2021-01-07
    Graham Campbell

    In 2018, it was shown that all finitely generated virtually Abelian groups have multiple context-free word problems, and it is still an open problem as to where to precisely place the word problems of hyperbolic groups in the formal language hierarchy. Motivated by this, we introduce a new language class, the parallel hyperedge replacement string languages, containing all multiple context-free and

    更新日期:2021-01-08
  • Logics of First-Order Constraints -- A Category Independent Approach
    arXiv.cs.LO Pub Date : 2021-01-06
    Uwe Wolter

    Reflecting our experiences in areas, like Algebraic Specifications, Abstract Model Theory, Graph Transformations, and Model Driven Software Engineering (MDSE), we present a general, category independent approach to Logics of First-Order Constraints (LFOC). Traditional First-Order Logic, Description Logic and the sketch framework are discussed as examples. We use the concept of institution [Diaconescu08

    更新日期:2021-01-07
  • Confluence up to Garbage in Graph Transformation
    arXiv.cs.LO Pub Date : 2021-01-06
    Graham Campbell; Detlef Plump

    The transformation of graphs and graph-like structures is ubiquitous in computer science. When a system is described by graph-transformation rules, it is often desirable that the rules are both terminating and confluent so that rule applications in an arbitrary order produce unique resulting graphs. However, there are application scenarios where the rules are not globally confluent but confluent on

    更新日期:2021-01-07
  • Positive first-order logic on words
    arXiv.cs.LO Pub Date : 2021-01-06
    Denis Kuperberg

    We study FO+, a fragment of first-order logic on finite words, where monadic predicates can only appear positively. We show that there is a FO-definable language that is monotone in monadic predicates but not definable in FO+. This provides a simple proof that Lyndon's preservation theorem fails on finite structures. We additionally show that given a regular language, it is undecidable whether it is

    更新日期:2021-01-07
  • Dynamic Preference Logic meets Iterated Belief Change: Representation Results and Postulates Characterization
    arXiv.cs.LO Pub Date : 2021-01-05
    Marlo Souza; Álvaro Moreira; Renata Vieira

    AGM's belief revision is one of the main paradigms in the study of belief change operations. Recently, several logics for belief and information change have been proposed in the literature and used to encode belief change operations in rich and expressive semantic frameworks. While the connections of AGM-like operations and their encoding in dynamic doxastic logics have been studied before by the work

    更新日期:2021-01-06
  • Quantitative Corner Case Feature Analysis of Hybrid Automata with ForFET$^{SMT}$
    arXiv.cs.LO Pub Date : 2020-12-30
    Antonio Anastasio Bruto da Costa; Pallab Dasgupta; Nikolaos Kekatos

    The analysis and verification of hybrid automata (HA) models against rich formal properties can be a challenging task. Existing methods and tools can mainly reason whether a given property is satisfied or violated. However, such qualitative answers might not provide sufficient information about the model behaviors. This paper presents the ForFET$^{SMT}$ tool which can be used to reason quantitatively

    更新日期:2021-01-06
  • Formal Game Grammar and Equivalence
    arXiv.cs.LO Pub Date : 2020-12-31
    Paul Riggins; David McPherson

    We develop methods to formally describe and compare games, in order to probe questions of game structure and design, and as a stepping stone to predicting player behavior from design patterns. We define a grammar-like formalism to describe finite discrete games without hidden information, allowing for randomness, and mixed sequential and simultaneous play. We make minimal assumptions about the form

    更新日期:2021-01-05
  • Scalable Online Conformance Checking Using Incremental Prefix-Alignment Computation
    arXiv.cs.LO Pub Date : 2020-12-22
    Daniel Schuster; Gero J. Kolhof

    Conformance checking techniques aim to collate observed process behavior with normative/modeled process models. The majority of existing approaches focuses on completed process executions, i.e., offline conformance checking. Recently, novel approaches have been designed to monitor ongoing processes, i.e., online conformance checking. Such techniques detect deviations of an ongoing process execution

    更新日期:2021-01-05
  • Verifying a Cruise Control System using Simulink and SpaceEx
    arXiv.cs.LO Pub Date : 2020-12-31
    Nikolaos Kekatos

    This article aims to provide a simple step-by-step guide highlighting the steps needed to verify a control system with formal verification tools. Starting from a description of the physical system and a control objective in natural language, we design the plant and the controller, we use Simulink for simulation and we employ a reachability analysis tool, SpaceEx, for formal verification.

    更新日期:2021-01-05
  • Computable Random Variables and Conditioning
    arXiv.cs.LO Pub Date : 2020-12-22
    Pieter Collins

    The aim of this paper is to present an elementary computable theory of random variables, based on the approach to probability via valuations. The theory is based on a type of lower-measurable sets, which are controlled limits of open sets, and extends existing work in this area by providing a computable theory of conditional random variables. The theory is based within the framework of type-two effectivity

    更新日期:2021-01-05
  • Text Searching Allowing for Non-Overlapping Adjacent Unbalanced Translocations
    arXiv.cs.LO Pub Date : 2021-01-03
    Domenico Cantone; Simone Faro; Arianna Pavone

    In this paper we investigate the \emph{approximate string matching problem} when the allowed edit operations are \emph{non-overlapping unbalanced translocations of adjacent factors}. Such kind of edit operations take place when two adjacent sub-strings of the text swap, resulting in a modified string. The two involved substrings are allowed to be of different lengths. Such large-scale modifications

    更新日期:2021-01-05
  • diff-SAT -- A Software for Sampling and Probabilistic Reasoning for SAT and Answer Set Programming
    arXiv.cs.LO Pub Date : 2021-01-03
    Matthias Nickles

    This paper describes diff-SAT, an Answer Set and SAT solver which combines regular solving with the capability to use probabilistic clauses, facts and rules, and to sample an optimal world-view (multiset of satisfying Boolean variable assignments or answer sets) subject to user-provided probabilistic constraints. The sampling process minimizes a user-defined differentiable objective function using

    更新日期:2021-01-05
  • If You're Happy, Then You Know It: The Logic of Happiness... and Sadness
    arXiv.cs.LO Pub Date : 2021-01-02
    Sanaz Azimipour; Pavel Naumov

    The article proposes a formal semantics of happiness and sadness modalities in imperfect information setting. It shows that these modalities are not definable through each other and gives a sound and complete axiomatization of their properties.

    更新日期:2021-01-05
  • Formalizing Hall's Marriage Theorem in Lean
    arXiv.cs.LO Pub Date : 2021-01-01
    Alena Gusakov; Bhavik Mehta; Kyle A. Miller

    We formalize Hall's Marriage Theorem in the Lean theorem prover for inclusion in mathlib, which is a community-driven effort to build a unified mathematics library for Lean. One goal of the mathlib project is to contain all of the topics of a complete undergraduate mathematics education. We provide three presentations of the main theorem statement: in terms of indexed families of finite sets, of relations

    更新日期:2021-01-05
  • Yet another argument in favour of NP=CoNP
    arXiv.cs.LO Pub Date : 2020-12-28
    Edward Hermann Haeusler

    This article shows yet another proof of NP=CoNP$. In a previous article, we proved that NP=PSPACE and from it we can conclude that NP=CoNP immediately. The former proof shows how to obtain polynomial and, polynomial in time checkable Dag-like proofs for all purely implicational Minimal logic tautologies. From the fact that Minimal implicational logic is PSPACE-complete we get the proof that NP=PSPACE

    更新日期:2021-01-05
  • A Detailed Account of The Inconsistent Labelling Problem of Stutter-Preserving Partial-Order Reduction
    arXiv.cs.LO Pub Date : 2020-12-31
    Thomas NeeleRoyal Holloway University of London; Antti ValmariUniversity of Jyväskylä; Tim A. C. WillemseEindhoven University of Technology

    One of the most popular state-space reduction techniques for model checking is partial-order reduction (POR). Of the many different POR implementations, stubborn sets are a very versatile variant and have thus seen many different applications over the past 32 years. One of the early stubborn sets works shows how the basic conditions for reduction can be augmented to preserve stutter-trace equivalence

    更新日期:2021-01-01
  • Synthesizing Approximate Implementations for Unrealizable Specifications
    arXiv.cs.LO Pub Date : 2020-12-29
    Rayna Dimitrova; Bernd Finkbeiner; Hazem Torfah

    The unrealizability of a specification is often due to the assumption that the behavior of the environment is unrestricted. In this paper, we present algorithms for synthesis in bounded environments, where the environment can only generate input sequences that are ultimately periodic words (lassos) with finite representations of bounded size. We provide automata-theoretic and symbolic approaches for

    更新日期:2021-01-01
  • Explainable Reactive Synthesis
    arXiv.cs.LO Pub Date : 2020-12-29
    Tom Baumeister; Bernd Finkbeiner; Hazem Torfah

    Reactive synthesis transforms a specification of a reactive system, given in a temporal logic, into an implementation. The main advantage of synthesis is that it is automatic. The main disadvantage is that the implementation is usually very difficult to understand. In this paper, we present a new synthesis process that explains the synthesized implementation to the user. The process starts with a simple

    更新日期:2021-01-01
  • Reachability relations of timed pushdown automata
    arXiv.cs.LO Pub Date : 2020-12-30
    Lorenzo Clemente; Sławomir Lasota

    Timed pushdown automata (TPDA) are an expressive formalism combining recursion with a rich logic of timing constraints. We prove that reachability relations of TPDA are expressible in linear arithmetic, a rich logic generalising Presburger arithmetic and rational arithmetic. The main technical ingredients are a novel quantifier elimination result for clock constraints (used to simplify the syntax of

    更新日期:2021-01-01
  • Commutative Information Algebras: Representation and Duality Theory
    arXiv.cs.LO Pub Date : 2020-12-30
    Juerg Kohlas; Juerg Schmid

    Information algebras arise from the idea that information comes in pieces which can be aggregated or combined into new pieces, that information refers to questions and that from any piece of information, the part relevant to a given question can be extracted. This leads to a certain type of algebraic structures, basically semilattices endowed with with additional unary operations. These operations

    更新日期:2021-01-01
  • Security Engineering for ISO 21434
    arXiv.cs.LO Pub Date : 2020-12-30
    Yuri Gil Dantas; Vivek Nigam; Harald Ruess

    The ISO 21434 is a new standard that has been proposed to address the future challenges of automotive cybersecurity. This white paper takes a closer look at the ISO 21434 helping engineers to understand the ISO 21434 parts, the key activities to be carried out and the main artefacts that shall be produced. As any certification, obtaining the ISO 21434 certification can be daunting at first sight. Engineers

    更新日期:2021-01-01
  • Approximate Automata for Omega-Regular Languages
    arXiv.cs.LO Pub Date : 2020-12-29
    Rayna Dimitrova; Bernd Finkbeiner; Hazem Torfah

    Automata over infinite words, also known as omega-automata, play a key role in the verification and synthesis of reactive systems. The spectrum of omega-automata is defined by two characteristics: the acceptance condition (e.g. B\"uchi or parity) and the determinism (e.g., deterministic or nondeterministic) of an automaton. These characteristics play a crucial role in applications of automata theory

    更新日期:2021-01-01
  • Canonical Representations of k-Safety Hyperproperties
    arXiv.cs.LO Pub Date : 2020-12-29
    Bernd Finkbeiner; Lennart Haas; Hazem Torfah

    Hyperproperties elevate the traditional view of trace properties form sets of traces to sets of sets of traces and provide a formalism for expressing information-flow policies. For trace properties, algorithms for verification, monitoring, and synthesis are typically based on a representation of the properties as omega-automata. For hyperproperties, a similar, canonical automata-theoretic representation

    更新日期:2021-01-01
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