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  • Property-Directed Verification of Recurrent Neural Networks
    arXiv.cs.FL Pub Date : 2020-09-22
    Igor Khmelnitsky; Daniel Neider; Rajarshi Roy; Benoît Barbot; Benedikt Bollig; Alain Finkel; Serge Haddad; Martin Leucker; Lina Ye

    This paper presents a property-directed approach to verifying recurrent neural networks (RNNs). To this end, we learn a deterministic finite automaton as a surrogate model from a given RNN using active automata learning. This model may then be analyzed using model checking as verification technique. The term property-directed reflects the idea that our procedure is guided and controlled by the given

  • Less Manual Work for Safety Engineers: Towards an Automated Safety Reasoning with Safety Patterns
    arXiv.cs.FL Pub Date : 2020-09-22
    Yuri Gil Dantasfortiss GmbH; Antoaneta Kondevafortiss GmbH; Vivek Nigamfortiss GmbH

    The development of safety-critical systems requires the control of hazards that can potentially cause harm. To this end, safety engineers rely during the development phase on architectural solutions, called safety patterns, such as safety monitors, voters, and watchdogs. The goal of these patterns is to control (identified) faults that can trigger hazards. Safety patterns can control such faults by

  • Grey-Box Learning of Register Automata
    arXiv.cs.FL Pub Date : 2020-09-21
    Bharat Garhewal; Frits Vaandrager; Falk Howar; Timo Schrijvers; Toon Lenaerts; Rob Smits

    Model learning (a.k.a. active automata learning) is a highly effective technique for obtaining black-box finite state models of software components. Thus far, generalisation to infinite state systems with inputs/outputs that carry data parameters has been challenging. Existing model learning tools for infinite state systems face scalability problems and can only be applied to restricted classes of

  • Random Expansion Method for the Generation of Complex Cellular Automata
    arXiv.cs.FL Pub Date : 2020-09-20
    Juan Carlos Seck-Tuoh-Mora; Norberto Hernandez-Romero; Joselito Medina-Marin; Genaro J. Martinez; Irving Barragan-Vite

    The emergence of complex behaviors in cellular automata is an area that has been widely developed in recent years with the intention to generate and analyze automata that produce space-moving patterns or gliders that interact in a periodic background. Frequently, this type of automata has been found through either an exhaustive search or a meticulous construction of the evolution rule. In this study

  • Proceedings 11th International Symposium on Games, Automata, Logics, and Formal Verification
    arXiv.cs.FL Pub Date : 2020-09-20
    Jean-Francois RaskinUniversité Libre de Bruxelles; Davide BresolinUniversità di Padova

    This volume contains the proceedings of the 11th International Symposium on Games, Automata, Logic and Formal Verification (GandALF 2020). The symposium took place as a fully online event on September 21-22, 2020. The GandALF symposium was established by a group of Italian computer scientists interested in mathematical logic, automata theory, game theory, and their applications to the specification

  • On complex dynamics from reversible cellular automata
    arXiv.cs.FL Pub Date : 2020-09-18
    Juan Carlos Seck-Tuoh-Mora; Genaro J. Martinez; Norberto Hernandez-Romero; Joselito Medina-Marin; Irving Barragan-Vite

    Complexity has been a recurrent research topic in cellular automata because they represent systems where complex behaviors emerge from simple local interactions. A significant amount of previous research has been conducted proposing instances of complex cellular automata; however, most of the proposed methods are based on a careful search or a meticulous construction of evolution rules. This paper

  • Bounded Model Checking for Hyperproperties
    arXiv.cs.FL Pub Date : 2020-09-18
    Tzu-Han Hsu; Cesar Sanchez; Borzoo Bonakdarpour

    This paper introduces the first bounded model checking (BMC) algorithm for hyperproperties expressed in HyperLTL. Just as the classic BMC technique for LTL primarily aiming at finding bugs, our approach also targets identifying counterexamples. LTL describes the property of individual traces and BMC for LTL is reduced to SAT solving. HyperLTL allows explicit and simultaneous quantification over traces

  • ACSS-q: Algorithmic complexity for short strings via quantum accelerated approach
    arXiv.cs.FL Pub Date : 2020-09-18
    Aritra Sarkar; Koen Bertels

    In this research we present a quantum circuit for estimating algorithmic complexity using the coding theorem method. This accelerates inferring algorithmic structure in data for discovering causal generative models. The computation model is restricted in time and space resources to make it computable in approximating the target metrics. The quantum circuit design based on our earlier work that allows

  • Typestates to Automata and back: a tool
    arXiv.cs.FL Pub Date : 2020-09-17
    André TrindadeNOVA School of Science and Technology; João MotaNOVA School of Science and Technology; António RavaraNOVA School of Science and Technology

    Development of software is an iterative process. Graphical tools to represent the relevant entities and processes can be helpful. In particular, automata capture well the intended execution flow of applications, and are thus behind many formal approaches, namely behavioral types. Typestate-oriented programming allow us to model and validate the intended protocol of applications, not only providing

  • Higher-Order Nonemptiness Step by Step
    arXiv.cs.FL Pub Date : 2020-09-17
    Paweł Parys

    We show a new simple algorithm that checks whether a given higher-order grammar generates a nonempty language of trees. The algorithm amounts to a procedure that transforms a grammar of order n to a grammar of order n-1, preserving nonemptiness, and increasing the size only exponentially. After repeating the procedure n times, we obtain a grammar of order 0, whose nonemptiness can be easily checked

  • An Abstract Framework for Choreographic Testing
    arXiv.cs.FL Pub Date : 2020-09-17
    Alex CotoGSSI; Roberto GuancialeKTH; Emilio TuostoGSSI

    We initiate the development of a model-driven testing framework for message-passing systems. The notion of test for communicating systems cannot simply be borrowed from existing proposals. Therefore, we formalize a notion of suitable distributed tests for a given choreography and devise an algorithm that generates tests as projections of global views. Our algorithm abstracts away from the actual projection

  • A categorical duality for algebras of partial functions
    arXiv.cs.FL Pub Date : 2020-09-16
    Brett McLean

    We prove a categorical duality between a class of abstract algebras of partial functions and a class of (small) topological categories. The algebras are the isomorphs of collections of partial functions closed under the operations of composition, antidomain, range, and preferential union (or 'override'). The topological categories are those whose space of objects is a Stone space, source map is a local

  • Automatic Trajectory Synthesis for Real-Time Temporal Logic
    arXiv.cs.FL Pub Date : 2020-09-14
    Rafael Rodrigues da Silva; Vince Kurtz; Hai Lin

    Many safety-critical systems must achieve high-level task specifications with guaranteed safety and correctness. Much recent progress towards this goal has been made through controller synthesis from temporal logic specifications. Existing approaches, however, have been limited to relatively short and simple specifications. Furthermore, existing methods either consider some prior discretization of

  • On Computability, Learnability and Extractability of Finite State Machines from Recurrent Neural Networks
    arXiv.cs.FL Pub Date : 2020-09-10
    Reda Marzouk

    This work aims at shedding some light on connections between finite state machines (FSMs), and recurrent neural networks (RNNs). Examined connections in this master's thesis is threefold: the extractability of finite state machines from recurrent neural networks, learnability aspects and computationnal links. With respect to the former, the long-standing clustering hypothesis of RNN hidden state space

  • Pushdown and Lempel-Ziv Depth
    arXiv.cs.FL Pub Date : 2020-09-10
    Liam Jordon; Philippe Moser

    This paper expands upon existing and introduces new formulations of Bennett's logical depth. In previously published work by Jordon and Moser, notions of finite-state-depth and pushdown-depth were examined and compared. These were based on finite-state transducers and information lossless pushdown compressors respectively. Unfortunately a full separation between the two notions was not established

  • Equations in virtually abelian groups: languages and growth
    arXiv.cs.FL Pub Date : 2020-09-08
    Alex Evetts; Alex Levine

    This paper explores the nature of the solution sets of systems of equations in virtually abelian groups. We view this question from two angles. From a formal language perspective, we prove that the set of solutions to a system of equations forms an EDT0L language, with respect to a natural normal form. Looking at growth, we show that the growth series of the language of solutions is rational. Furthermore

  • On prefix palindromic length of automatic words
    arXiv.cs.FL Pub Date : 2020-09-07
    Anna E. Frid; Enzo Laborde; Jarkko Peltomäki

    The prefix palindromic length $\mathrm{PPL}_{\mathbf{u}}(n)$ of an infinite word $\mathbf{u}$ is the minimal number of concatenated palindromes needed to express the prefix of length $n$ of $\mathbf{u}$. Since 2013, it is still unknown if $\mathrm{PPL}_{\mathbf{u}}(n)$ is unbounded for every aperiodic infinite word $\mathbf{u}$, even though this has been proven for almost all aperiodic words. At the

  • A small-step approach to multi-trace checking against interactions
    arXiv.cs.FL Pub Date : 2020-09-03
    Erwan Mahe; Boutheina Bannour; Christophe Gaston; Arnault Lapitre; Pascale Le Gall

    Interaction models describe the exchange of messages between the different components of distributed systems. We have previously defined a small-step operational semantics for interaction models. The paper extends this work by presenting an approach for checking the validity of multi-traces against interaction models. A multi-trace is a collection of traces (sequences of emissions and receptions),

  • Notes on Equivalence and Minimization of Weighted Automata
    arXiv.cs.FL Pub Date : 2020-09-02
    Stefan Kiefer

    This set of notes re-proves known results on weighted automata (over a field, also known as multiplicity automata). The text offers a unified view on theorems and proofs that have appeared in the literature over decades and were written in different styles and contexts. None of the results reported here are claimed to be new. The content centres around fundamentals of equivalence and minimization,

  • Tree Automata for Extracting Consensus from Partial Replicas of a Structured Document
    arXiv.cs.FL Pub Date : 2020-09-02
    Maurice Tchoupé Tchendji; Milliam Maxime Zekeng Ndadji

    In an asynchronous cooperative editing workflow of a structured document, each of the co-authors receives in the different phases of the editing process, a copy of the document to insert its contribution. For confidentiality reasons, this copy may be only a partial replica containing only parts of the (global) document which are of demonstrated interest for the considered co-author. Note that some

  • Closure under Coupling of Cellular-DEVS for the Optimization of Memory Resource: Wildfire Spread Case Study
    arXiv.cs.FL Pub Date : 2020-09-01
    Youcef Dahmani; Maamar El Amine Hamri; Nesrine Driouche

    The present work aims to show one of the advantages of using the property of closure under coupling in the DEVS specification. The advantage concerned in this paper attempts to address the need for memory resources during the simulation of systems by cellular-DEVS. This improvement of performance is based on the usage of the property closure under coupling in the DEVS formalism. With this property

  • Recognition and Complexity Results for Projection Languages of Two-Dimensional Automata
    arXiv.cs.FL Pub Date : 2020-09-01
    Taylor J. Smith; Kai Salomaa

    The row projection (resp., column projection) of a two-dimensional language $L$ is the one-dimensional language consisting of all first rows (resp., first columns) of each two-dimensional word in $L$. The operation of row projection has previously been studied under the name "frontier language", and previous work has focused on one- and two-dimensional language classes. In this paper, we study projections

  • Computability by Monadic Second-Order Logic
    arXiv.cs.FL Pub Date : 2020-08-27
    Joost Engelfriet

    A binary relation on graphs is recursively enumerable if and only if it can be computed by a formula in monadic second-order logic. The latter means that the formula defines a set of graphs, in the usual way, such that each "computation graph" in that set determines a pair consisting of an input graph and an output graph.

  • Languages recognised by finite semigroups, and their generalisations to objects such as trees and graphs, with an emphasis on definability in monadic second-order logic
    arXiv.cs.FL Pub Date : 2020-08-26
    Mikołaj Bojańczyk

    These are lecture notes on the algebraic approach to regular languages. The classical algebraic approach is for finite words; it uses semigroups instead of automata. However, the algebraic approach can be extended to structures beyond words, e.g.~infinite words, or trees or graphs. The purpose of this book is to describe the algebraic approach in a way that covers these extensions.

  • Optimal Strategies in Weighted Limit Games (full version)
    arXiv.cs.FL Pub Date : 2020-08-26
    Aniello Murano; Sasha Rubin; Martin Zimmermann

    We prove the existence and computability of optimal strategies in weighted limit games, zero-sum infinite-duration games with a B\"uchi-style winning condition requiring to produce infinitely many play prefixes that satisfy a given regular specification. Quality of plays is measured in the maximal weight of infixes between successive play prefixes that satisfy the specification.

  • Concatenation Operations and Restricted Variants of Two-Dimensional Automata
    arXiv.cs.FL Pub Date : 2020-08-25
    Taylor J. Smith; Kai Salomaa

    A two-dimensional automaton operates on arrays of symbols. While a standard (four-way) two-dimensional automaton can move its input head in four directions, restricted two-dimensional automata are only permitted to move their input heads in three or two directions; these models are called three-way and two-way two-dimensional automata, respectively. In two dimensions, we may extend the notion of concatenation

  • Automated Trajectory Synthesis for UAV Swarms Based on Resilient Data Collection Objectives
    arXiv.cs.FL Pub Date : 2020-08-25
    A H M Jakaria; Mohammad Ashiqur Rahman; Matthew Anderson; Steven Drager

    The use of Unmanned Aerial Vehicles (UAVs) for collecting data from remotely located sensor systems is emerging. The data can be time-sensitive and require to be transmitted to a data processing center. However, planning the trajectory of a collaborative UAV swarm depends on multi-fold constraints, such as data collection requirements, UAV maneuvering capacity, and budget limitation. Since a UAV may

  • Entropia: A Family of Entropy-Based Conformance Checking Measures for Process Mining
    arXiv.cs.FL Pub Date : 2020-08-21
    Artem Polyvyanyy; Hanan Alkhammash; Claudio Di Ciccio; Luciano García-Bañuelos; Anna Kalenkova; Sander J. J. Leemans; Jan Mendling; Alistair Moffat; Matthias Weidlich

    This paper presents a command-line tool, called Entropia, that implements a family of conformance checking measures for process mining founded on the notion of entropy from information theory. The measures allow quantifying classical non-deterministic and stochastic precision and recall quality criteria for process models automatically discovered from traces executed by IT-systems and recorded in their

  • Visual Designing and Debugging of Deterministic Finite-State Machines in FSM
    arXiv.cs.FL Pub Date : 2020-08-21
    Marco T. MorazánSeton Hall University; Joshua M. SchappelSeton Hall University; Sachin MahashabdeSeton Hall University

    This article presents a visualization tool for designing and debugging deterministic finite-state machines in FSM -- a domain specific language for the automata theory classroom. Like other automata visualization tools, users can edit machines and observe their execution, given some input. Unlike other automata visualization tools, the user is not burdened nor distracted with rendering a machine as

  • On the Use of Quasiorders in Formal Language Theory
    arXiv.cs.FL Pub Date : 2020-08-20
    Pedro Valero

    In this thesis we use quasiorders on words to offer a new perspective on two well-studied problems from Formal Language Theory: deciding language inclusion and manipulating the finite automata representations of regular languages. First, we present a generic quasiorder-based framework that, when instantiated with different quasiorders, yields different algorithms (some of them new) for deciding language

  • Novel Results on the Number of Runs of the Burrows-Wheeler-Transform
    arXiv.cs.FL Pub Date : 2020-08-19
    Sara Giuliani; Shunsuke Inenaga; Zsuzsanna Lipták; Nicola Prezza; Marinella Sciortino; Anna Toffanello

    The Burrows-Wheeler-Transform (BWT), a reversible string transformation, is one of the fundamental components of many current data structures in string processing. It is central in data compression, as well as in efficient query algorithms for sequence data, such as webpages, genomic and other biological sequences, or indeed any textual data. The BWT lends itself well to compression because its number

  • Abelian Closures of Infinite Binary Words
    arXiv.cs.FL Pub Date : 2020-08-18
    Svetlana Puzynina; Markus A. Whiteland

    Two finite words $u$ and $v$ are called Abelian equivalent if each letter occurs equally many times in both $u$ and $v$. The abelian closure $\mathcal{A}(\mathbf{x})$ of (the shift orbit closure of) an infinite word $\mathbf{x}$ is the set of infinite words $\mathbf{y}$ such that, for each factor $u$ of $\mathbf{y}$, there exists a factor $v$ of $\mathbf{x}$ which is abelian equivalent to $u$. The

  • On the Power of Automata Minimization in Temporal Synthesis
    arXiv.cs.FL Pub Date : 2020-08-15
    Shufang Zhu; Lucas M. Tabajara; Geguang Pu; Moshe Y. Vardi

    Reactive synthesis is the problem of automatically constructing a reactive system from a formal specification, with the guarantee that the executions of the system align with the specification. The specification is often described in temporal logic. Some types of specifications can be converted into deterministic finite automata (DFA) as an intermediate step in synthesis, thus benefiting from the fact

  • Automatic Translation of tock-CSP into Timed Automata
    arXiv.cs.FL Pub Date : 2020-08-16
    Abdulrazaq Abba; Ana Cavalcanti; Jeremy Jacob

    The process algebra tock-CSP provides textual notations for modelling discrete-time behaviours, with the support of various tools for verification. Similarly, automatic verification of Timed Automata (TA) is supported by the real-time verification toolbox UPPAAL. TA and tock-CSP differ in both modelling and verification approaches. For instance, liveness requirements are difficult to specify with the

  • Stronger Lower Bounds for Polynomial Time Problems
    arXiv.cs.FL Pub Date : 2020-08-15
    András Z. Salamon; Michael Wehar

    We reinvestigate the classical topic of limited nondeterminism, to prove stronger conditional lower bounds for polynomial time problems. In particular, we show that CircuitSAT for circuits with m gates and log(m) inputs (denoted by log-CircuitSAT) is not solvable in quasilinear time unless the exponential time hypothesis (ETH) is false. In other words, a polynomial time improvement for log-CircuitSAT

  • An Efficient Model Inference Algorithm for Learning-based Testing of Reactive Systems
    arXiv.cs.FL Pub Date : 2020-08-14
    Muddassar A. Sindhu

    Learning-based testing (LBT) is an emerging methodology to automate iterative black-box requirements testing of software systems. The methodology involves combining model inference with model checking techniques. However, a variety of optimisations on model inference are necessary in order to achieve scalable testing for large systems. In this paper we describe the IKL learning algorithm which is an

  • Resilient Abstraction-Based Controller Design
    arXiv.cs.FL Pub Date : 2020-08-14
    Stanly SamuelIndian Institute of Science; Kaushik MallikMax Planck Institute for Software Systems; Anne-Kathrin SchmuckMax Planck Institute for Software Systems; Daniel NeiderMax Planck Institute for Software Systems

    We consider the computation of resilient controllers for perturbed non-linear dynamical systems w.r.t. linear-time temporal logic specifications. We address this problem through the paradigm of Abstraction-Based Controller Design (ABCD) where a finite state abstraction of the perturbed system dynamics is constructed and utilized for controller synthesis. In this context, our contribution is twofold:

  • State Complexity Bounds for Shuffle and Iterated Shuffle Combined with the Commutative Closure on Group Languages
    arXiv.cs.FL Pub Date : 2020-08-12
    Stefan Hoffmann

    We show that the shuffle and iterated shuffle of the commutative closure of a group language is regular, and derive state bounds for resulting automata. In particular, for commutative group languages the iterated shuffle is a regularity preserving operation. For the shuffle of two commutative group languages, we give a sharp bound. For applying the shuffle operation to the commutative closure of multiple

  • Reactive Synthesis from Extended Bounded Response LTL Specifications
    arXiv.cs.FL Pub Date : 2020-08-12
    Alessandro Cimatti; Luca Geatti; Nicola Gigante; Angelo Montanari; Stefano Tonetta

    Reactive synthesis is a key technique for the design of correct-by-construction systems and has been thoroughly investigated in the last decades. It consists in the synthesis of a controller that reacts to environment's inputs satisfying a given temporal logic specification. Common approaches are based on the explicit construction of automata and on their determinization, which limit their scalability

  • On the number of useful objects in P systems with active membranes
    arXiv.cs.FL Pub Date : 2020-08-11
    Zsolt Gazdag; Károly Hajagos; Szabolcs Iván

    In this paper we investigate the number of objects actually used in the terminating computations of a certain variant of polarizationless P systems with active membranes. The P systems we consider here have no in-communication rules and have no different rules triggered by the same object to manipulate the same membrane. We show that if we consider such a P system $\Pi$ and its terminating computation

  • An Ansatz for undecidable computation in RNA-world automata
    arXiv.cs.FL Pub Date : 2020-08-12
    Adam J. Svahn; Mikhail Prokopenko

    In this Ansatz we consider theoretical constructions of RNA polymers into automata, a form of computational structure. The basis for transitions in our automata are plausible RNA-world enzymes that may perform ligation or cleavage. Limited to these operations, we construct RNA automata of increasing complexity; from the Finite Automaton (RNA-FA) to the Turing Machine equivalent 2-stack PDA (RNA-2PDA)

  • Automata and finite order elements in the Nottingham group
    arXiv.cs.FL Pub Date : 2020-08-11
    Jakub Byszewski; Gunther Cornelissen; Djurre Tijsma

    The Nottingham group at 2 is the group of (formal) power series $t+a_2 t^2+ a_3 t^3+ \cdots$ in the variable $t$ with coefficients $a_i$ from the field with two elements, where the group operation is given by composition of power series. The depth of such a series is the largest $d\geq 1$ for which $a_2=\dots=a_d=0$. Only a handful of power series of finite order are explicitly known through a formula

  • On the Complexity of the Universality and Inclusion Problems for Unambiguous Context-Free Grammars
    arXiv.cs.FL Pub Date : 2020-08-07
    Lorenzo ClementeUniversity of Warsaw

    We study the computational complexity of universality and inclusion problems for unambiguous finite automata and context-free grammars. We observe that several such problems can be reduced to the universality problem for unambiguous context-free grammars. The latter problem has long been known to be decidable and we propose a PSPACE algorithm that works by reduction to the zeroness problem of recurrence

  • SafetyOps
    arXiv.cs.FL Pub Date : 2020-08-11
    Umair Siddique

    Safety assurance is a paramount factor in the large-scale deployment of various autonomous systems (e.g., self-driving vehicles). However, the execution of safety engineering practices and processes have been challenged by an increasing complexity of modern safety-critical systems. This attribute has become more critical for autonomous systems that involve artificial intelligence (AI) and data-driven

  • Verifying Safety Properties of Inductively Defined Parameterized Systems
    arXiv.cs.FL Pub Date : 2020-08-10
    Marius Bozga; Radu Iosif

    We introduce a term algebra as a new formal specification language for the architectures of distributed systems consisting of a finite yet unbounded number of components. The language allows to describe infinite sets of architectures that share the same pattern, using a set of recursive definitions, similar to the ones used to describe algebraic data types. Further, we give a verification method for

  • Blocksequences of k-local Words
    arXiv.cs.FL Pub Date : 2020-08-08
    Pamela Fleischmann; Lukas Haschke; Florin Manea; Dirk Nowotka; Cedric Tsatia Tsida; Judith Wiedenbeck

    The locality of words is a relatively young structural complexity measure, introduced by Day et al. in 2017 in order to define classes of patterns with variables which can be matched in polynomial time. The main tool used to compute the locality of a word is called marking sequence: an ordering of the distinct letters occurring in the respective order. Once a marking sequence is defined, the letters

  • From Quasi-Dominions to Progress Measures
    arXiv.cs.FL Pub Date : 2020-08-10
    Massimo Benerecetti; Daniele Dell'Erba; Marco Faella; Fabio Mogavero

    In this paper we revisit the approaches to the solution of parity games based on progress measures and show how the notion of quasi dominions can be integrated with those approaches. The idea is that, while progress measure based techniques typically focus on one of the two players, little information is gathered on the other player during the solution process. Adding quasi dominions provides additional

  • Safe and efficient collision avoidance control for autonomous vehicles
    arXiv.cs.FL Pub Date : 2020-08-10
    Qiang Wang; Dachuan Li; Joseph Sifakis

    We study a novel principle for safe and efficient collision avoidance that adopts a mathematically elegant and general framework making as much as possible abstraction of the controlled vehicle's dynamics and of its environment. Vehicle dynamics is characterized by pre-computed functions for accelerating and braking to a given speed. Environment is modeled by a function of time giving the free distance

  • From Well Structured Transition Systems to Program Verification
    arXiv.cs.FL Pub Date : 2020-08-07
    Alain FinkelUniversite Paris-Saclay, ENS Paris-Saclay, CNRS

    We describe the use of the theory of WSTS for verifying programs.

  • Cayley Polynomial-Time Computable Groups
    arXiv.cs.FL Pub Date : 2020-08-06
    Dmitry Berdinsky; Murray Elder; Prohrak Kruengthomya

    We propose a new generalisation of Cayley automatic groups, varying the time complexity of computing multiplication, and language complexity of the normal form representatives. We first consider groups which have normal form language in the class $\mathcal C$ and multiplication by generators computable in linear time on a certain restricted Turing machine model (position-faithful one-tape). We show

  • Glushkov's construction for functional subsequential transducers
    arXiv.cs.FL Pub Date : 2020-08-05
    Aleksander Mendoza-Drosik

    Glushkov's construction has many interesting properties, however, they become even more evident when applied to transducers. This article strives to show the unusual link between functional subsequential finite state transducers and Glushkov's construction. The methods and algorithms presented here were used to implement compiler of regular expressions.

  • The Intersection of $3$-Maximal Submonids
    arXiv.cs.FL Pub Date : 2020-08-04
    Giuseppa Castiglione; Štěpán Holub

    Very little is known about the structure of the intersection of two $k$-generated monoids of words, even for $k=3$. Here we investigate the case of $k$-maximal monoids, that is, monoids whose basis of cardinality $k$ cannot be non-trivially decomposed into at most $k$ words. We characterize the intersection in the case of two $3$-maximal monoids.

  • Asymptotic Approximation by Regular Languages
    arXiv.cs.FL Pub Date : 2020-08-04
    Ryoma Sin'ya

    This paper investigates a new property of formal languages called REG-measurability where REG is the class of regular languages. Intuitively, a language \(L\) is REG-measurable if there exists an infinite sequence of regular languages that "converges" to \(L\). A language without REG-measurability has a complex shape in some sense so that it can not be (asymptotically) approximated by regular languages

  • Verifying Pufferfish Privacy in Hidden Markov Models
    arXiv.cs.FL Pub Date : 2020-08-04
    Depeng Liu; Bow-yaw Wang; Lijun Zhang

    Pufferfish is a Bayesian privacy framework for designing and analyzing privacy mechanisms. It refines differential privacy, the current gold standard in data privacy, by allowing explicit prior knowledge in privacy analysis. Through these privacy frameworks, a number of privacy mechanisms have been developed in literature. In practice, privacy mechanisms often need be modified or adjusted to specific

  • On the Expressive Power of Higher-Order Pushdown Systems
    arXiv.cs.FL Pub Date : 2020-08-03
    Paweł Parys

    We show that deterministic collapsible pushdown automata of second order can recognize a language that is not recognizable by any deterministic higher-order pushdown automaton (without collapse) of any order. This implies that there exists a tree generated by a second order collapsible pushdown system (equivalently, by a recursion scheme of second order) that is not generated by any deterministic higher-order

  • Theta palindromes in theta conjugates
    arXiv.cs.FL Pub Date : 2020-08-01
    Kalpana Mahalingam; Palak Pandoh; Anuran Maity

    A DNA string is a Watson-Crick (WK) palindrome when the complement of its reverse is equal to itself. The Watson-Crick mapping $\theta$ is an involution that is also an antimorphism. $\theta$-conjugates of a word is a generalisation of conjugates of a word that incorporates the notion of WK-involution $\theta$. In this paper, we study the distribution of palindromes and Watson-Crick palindromes, also

  • Implicit automata in typed $λ$-calculi II: streaming transducers vs categorical semantics
    arXiv.cs.FL Pub Date : 2020-08-03
    Lê Thành DũngTito; Nguyên; Camille Noûs; Pierre Pradic

    We characterize regular string transductions as programs in a linear $\lambda$-calculus with additives. One direction of this equivalence is proved by encoding copyless streaming string transducers (SSTs), which compute regular functions, into our $\lambda$-calculus. For the converse, we consider a categorical framework for defining automata and transducers over words, which allows us to relate register

  • MDA Models and PIM/PSM Transformations Using Extended Automata
    arXiv.cs.FL Pub Date : 2020-08-02
    David Dayan; Rivka Kaplinsky; Aryeh Wiesen; Simon Bloch

    This paper proposes a model of execution platform for the OMG request of a generic PlatformIndependent-Model (PIM) allowing realization of the Model Driven Architecture (MDA) standard. We propose AMDA (Automata based MDA), a method based on the use of parallel automata, which can be a common tool for building a PIM from UML diagrams (including OCL) and transforming the PIM to PSM automata and further

  • A note on the class of languages generated by F-systems over regular languages
    arXiv.cs.FL Pub Date : 2020-07-30
    Jorge C. Lucero

    An F-system is a computational model that performs a folding operation on strings of a given language, following directions coded on strings of another given language. This note considers the case in which both given languages are regular, and it shows that such F-system generates linear context-free languages. The demonstration is based on constructing a one-turn pushdown automaton for the generated

  • Dimension Groups and Dynamical Systems
    arXiv.cs.FL Pub Date : 2020-07-30
    Fabien Durand; Dominique Perrin

    We give a description of the link between topological dynamical systems and their dimension groups. The focus is on minimal systems and, in particular, on substitution shifts. We describe in detail the various classes of systems including Sturmian shifts and interval exchange shifts.

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