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  • ICE-Based Refinement Type Discovery for Higher-Order Functional Programs
    J. Autom. Reason. (IF 1.431) Pub Date : 2020-08-01
    Adrien Champion, Tomoya Chiba, Naoki Kobayashi, Ryosuke Sato

    We propose a method for automatically finding refinement types of higher-order function programs. Our method is an extension of the Ice framework of Garg et al. for finding invariants. In addition to the usual positive and negative samples in machine learning, their Ice framework uses implication constraints, which consist of pairs (x, y) such that if x satisfies an invariant, so does y. From these

  • Simulating Strong Practical Proof Systems with Extended Resolution
    J. Autom. Reason. (IF 1.431) Pub Date : 2020-07-31
    Benjamin Kiesl, Adrián Rebola-Pardo, Marijn J. H. Heule, Armin Biere

    Proof systems for propositional logic provide the basis for decision procedures that determine the satisfiability status of logical formulas. While the well-known proof system of extended resolution—introduced by Tseitin in the sixties—allows for the compact representation of proofs, modern SAT solvers (i.e., tools for deciding propositional logic) are based on different proof systems that capture

  • Multi-cost Bounded Tradeoff Analysis in MDP
    J. Autom. Reason. (IF 1.431) Pub Date : 2020-07-28
    Arnd Hartmanns, Sebastian Junges, Joost-Pieter Katoen, Tim Quatmann

    We provide a memory-efficient algorithm for multi-objective model checking problems on Markov decision processes (MDPs) with multiple cost structures. The key problem at hand is to check whether there exists a scheduler for a given MDP such that all objectives over cost vectors are fulfilled. We cover multi-objective reachability and expected cost objectives, and combinations thereof. We further transfer

  • Automated Proof of Bell–LaPadula Security Properties
    J. Autom. Reason. (IF 1.431) Pub Date : 2020-07-27
    Maximiliano Cristiá, Gianfranco Rossi

    Almost 50 years ago, D. E. Bell and L. LaPadula published the first formal model of a secure system, known today as the Bell–LaPadula (BLP) model. BLP is described as a state machine by means of first-order logic and set theory. The authors also formalize two state invariants known as security condition and *-property. Bell and LaPadula prove that all the state transitions preserve these invariants

  • Chain Reduction for Binary and Zero-Suppressed Decision Diagrams
    J. Autom. Reason. (IF 1.431) Pub Date : 2020-07-21
    Randal E. Bryant

    Chain reduction enables reduced ordered binary decision diagrams (BDDs) and zero-suppressed binary decision diagrams (ZDDs) to each take advantage of the other’s ability to symbolically represent Boolean functions in compact form. For any Boolean function, its chain-reduced ZDD (CZDD) representation will be no larger than its ZDD representation, and at most twice the size of its BDD representation

  • Decidable $${\exists }^*{\forall }^*$$ ∃ ∗ ∀ ∗ First-Order Fragments of Linear Rational Arithmetic with Uninterpreted Predicates
    J. Autom. Reason. (IF 1.431) Pub Date : 2020-07-18
    Marco Voigt

    First-order linear rational arithmetic enriched with uninterpreted predicates yields an interesting and very expressive modeling language. However, already the presence of a single uninterpreted predicate symbol of arity one or greater renders the associated satisfiability problem undecidable. We identify two decidable fragments, both based on the Bernays–Schönfinkel–Ramsey prefix class. Due to the

  • CoCon: A Conference Management System with Formally Verified Document Confidentiality
    J. Autom. Reason. (IF 1.431) Pub Date : 2020-07-16
    Andrei Popescu, Peter Lammich, Ping Hou

    We present a case study in formally verified security for realistic systems: the information flow security verification of the functional kernel of a web application, the CoCon conference management system. We use the Isabelle theorem prover to specify and verify fine-grained confidentiality properties, as well as complementary safety and “traceback” properties. The challenges posed by this development

  • Fine-Grained Complexity of Safety Verification
    J. Autom. Reason. (IF 1.431) Pub Date : 2020-07-14
    Peter Chini, Roland Meyer, Prakash Saivasan

    We study the fine-grained complexity of Leader Contributor Reachability (\({\textsf {LCR}} \)) and Bounded-Stage Reachability (\({\textsf {BSR}} \)), two variants of the safety verification problem for shared memory concurrent programs. For both problems, the memory is a single variable over a finite data domain. Our contributions are new verification algorithms and lower bounds. The latter are based

  • A Learning-Based Approach to Synthesizing Invariants for Incomplete Verification Engines
    J. Autom. Reason. (IF 1.431) Pub Date : 2020-07-13
    Daniel Neider, P. Madhusudan, Shambwaditya Saha, Pranav Garg, Daejun Park

    We propose a framework for synthesizing inductive invariants for incomplete verification engines, which soundly reduce logical problems in undecidable theories to decidable theories. Our framework is based on the counterexample guided inductive synthesis principle and allows verification engines to communicate non-provability information to guide invariant synthesis. We show precisely how the verification

  • Parameterized Model Checking on the TSO Weak Memory Model
    J. Autom. Reason. (IF 1.431) Pub Date : 2020-06-27
    Sylvain Conchon, David Declerck, Fatiha Zaïdi

    We present an extended version of the model checking modulo theories framework for verifying parameterized systems under the TSO weak memory model. Our extension relies on three main ingredients: (1) an axiomatic theory of the TSO memory model based on relations over (read, write) events, (2) a TSO-specific backward reachability algorithm and (3) an SMT solver for reasoning about TSO formulas. One

  • Constructive Decision via Redundancy-Free Proof-Search
    J. Autom. Reason. (IF 1.431) Pub Date : 2020-06-24
    Dominique Larchey-Wendling

    We give a constructive account of Kripke–Curry’s method which was used to establish the decidability of implicational relevance logic (\(\mathbf{R}_{{\rightarrow }}\)). To sustain our approach, we mechanize this method in axiom-free Coq, abstracting away from the specific features of \(\mathbf{R}_{{\rightarrow }}\) to keep only the essential ingredients of the technique. In particular we show how to

  • Formalizing Bachmair and Ganzinger’s Ordered Resolution Prover
    J. Autom. Reason. (IF 1.431) Pub Date : 2020-06-17
    Anders Schlichtkrull, Jasmin Blanchette, Dmitriy Traytel, Uwe Waldmann

    We present an Isabelle/HOL formalization of the first half of Bachmair and Ganzinger’s chapter on resolution theorem proving, culminating with a refutationally complete first-order prover based on ordered resolution with literal selection. We developed general infrastructure and methodology that can form the basis of completeness proofs for related calculi, including superposition. Our work clarifies

  • Formalizing the LLL Basis Reduction Algorithm and the LLL Factorization Algorithm in Isabelle/HOL
    J. Autom. Reason. (IF 1.431) Pub Date : 2020-06-09
    René Thiemann, Ralph Bottesch, Jose Divasón, Max W. Haslbeck, Sebastiaan J. C. Joosten, Akihisa Yamada

    The LLL basis reduction algorithm was the first polynomial-time algorithm to compute a reduced basis of a given lattice, and hence also a short vector in the lattice. It approximates an NP-hard problem where the approximation quality solely depends on the dimension of the lattice, but not the lattice itself. The algorithm has applications in number theory, computer algebra and cryptography. In this

  • Probably Partially True: Satisfiability for Łukasiewicz Infinitely-Valued Probabilistic Logic and Related Topics
    J. Autom. Reason. (IF 1.431) Pub Date : 2020-06-06
    Marcelo Finger, Sandro Preto

    We study probabilistic-logic reasoning in a context that allows for “partial truths”, focusing on computational and algorithmic properties of non-classical Łukasiewicz Infinitely-valued Probabilistic Logic. In particular, we study the satisfiability of joint probabilistic assignments, which we call ŁIPSAT. Although the search space is initially infinite, we provide linear algebraic methods that guarantee

  • Proof-Producing Synthesis of CakeML from Monadic HOL Functions
    J. Autom. Reason. (IF 1.431) Pub Date : 2020-06-06
    Oskar Abrahamsson, Son Ho, Hrutvik Kanabar, Ramana Kumar, Magnus O. Myreen, Michael Norrish, Yong Kiam Tan

    We introduce an automatic method for producing stateful ML programs together with proofs of correctness from monadic functions in HOL. Our mechanism supports references, exceptions, and I/O operations, and can generate functions manipulating local state, which can then be encapsulated for use in a pure context. We apply this approach to several non-trivial examples, including the instruction encoder

  • Unbounded-Time Safety Verification of Guarded LTI Models with Inputs by Abstract Acceleration
    J. Autom. Reason. (IF 1.431) Pub Date : 2020-05-29
    Dario Cattaruzza, Alessandro Abate, Peter Schrammel, Daniel Kroening

    Reachability analysis of dynamical models is a relevant problem that has seen much progress in the last decades, however with clear limitations pertaining to the nature of the dynamics and the soundness of the results. This article focuses on sound safety verification of unbounded-time (infinite-horizon) linear time-invariant (LTI) models with inputs using reachability analysis. We achieve this using

  • Building Strategies into QBF Proofs
    J. Autom. Reason. (IF 1.431) Pub Date : 2020-05-22
    Olaf Beyersdorff, Joshua Blinkhorn, Meena Mahajan

    Strategy extraction is of great importance for quantified Boolean formulas (QBF), both in solving and proof complexity. So far in the QBF literature, strategy extraction has been algorithmically performed from proofs. Here we devise the first QBF system where (partial) strategies are built into the proof and are piecewise constructed by simple operations along with the derivation. This has several

  • From QBFs to MALL and Back via Focussing
    J. Autom. Reason. (IF 1.431) Pub Date : 2020-05-22
    Anupam Das

    In this work we investigate how to extract alternating time bounds from ‘focussed’ proof systems. Our main result is the obtention of fragments of \(\mathsf {MALL} {\mathsf {w} }\) (\(\mathsf {MALL} \) with weakening) complete for each level of the polynomial hierarchy. In one direction we encode QBF satisfiability and in the other we encode focussed proof search, and we show that the composition of

  • Formalization of the Poincaré Disc Model of Hyperbolic Geometry
    J. Autom. Reason. (IF 1.431) Pub Date : 2020-04-30
    Danijela Simić, Filip Marić, Pierre Boutry

    We describe formalization of the Poincaré disc model of hyperbolic geometry within the Isabelle/HOL proof assistant. The model is defined within the complex projective line \(\mathbb {C}{}P^1\)and is shown to satisfy Tarski’s axioms except for Euclid’s axiom—it is shown to satisfy it’s negation, and, moreover, to satisfy the existence of limiting parallels axiom.

  • Formalization of Euler–Lagrange Equation Set Based on Variational Calculus in HOL Light
    J. Autom. Reason. (IF 1.431) Pub Date : 2020-03-06
    Yong Guan, Jingzhi Zhang, Guohui Wang, Ximeng Li, Zhiping Shi, Yongdong Li

    As the theoretical foundation of Lagrangian mechanics, Euler–Lagrange equation sets are widely applied in building mathematical models of physical systems, especially in solving dynamics problems. However, their preconditions are often not fully satisfied in practice. Therefore, it is necessary to verify their applications. The purpose of the present work is to conduct such verification by establishing

  • SPASS-AR: A First-Order Theorem Prover Based on Approximation-Refinement into the Monadic Shallow Linear Fragment
    J. Autom. Reason. (IF 1.431) Pub Date : 2020-02-25
    Andreas Teucke, Christoph Weidenbach

    We introduce FO-AR, an approximation-refinement approach for first-order theorem proving based on counterexample-guided abstraction refinement. A given first-order clause set N is transformed into an over-approximation \(N^{\prime }\) in a decidable first-order fragment. That means if \(N^{\prime }\) is satisfiable so is N. However, if \(N^{\prime }\) is unsatisfiable, then the approximation provides

  • Theorem Proving for Pointwise Metric Temporal Logic Over the Naturals via Translations
    J. Autom. Reason. (IF 1.431) Pub Date : 2020-02-19
    Ullrich Hustadt, Ana Ozaki, Clare Dixon

    We study translations from metric temporal logic (MTL) over the natural numbers to linear temporal logic (LTL). In particular, we present two approaches for translating from MTL to LTL which preserve the ExpSpace complexity of the satisfiability problem for MTL. In each of these approaches we consider the case where the mapping between states and time points is given by (i) a strict monotonic function

  • Verified Analysis of Random Binary Tree Structures
    J. Autom. Reason. (IF 1.431) Pub Date : 2020-02-08
    Manuel Eberl, Max W. Haslbeck, Tobias Nipkow

    This work is a case study of the formal verification and complexity analysis of some famous probabilistic algorithms and data structures in the proof assistant Isabelle/HOL. In particular, we consider the expected number of comparisons in randomised quicksort, the relationship between randomised quicksort and average-case deterministic quicksort, the expected shape of an unbalanced random Binary Search

  • Graph Theory in Coq: Minors, Treewidth, and Isomorphisms
    J. Autom. Reason. (IF 1.431) Pub Date : 2020-01-31
    Christian Doczkal, Damien Pous

    We present a library for graph theory in Coq/Ssreflect. This library covers various notions on simple graphs, directed graphs, and multigraphs. We use it to formalize several results from the literature: Menger’s theorem, the excluded-minor characterization of treewidth-two graphs, and a correspondence between multigraphs of treewidth at most two and terms of certain algebras.

  • Formal Reasoning Under Cached Address Translation
    J. Autom. Reason. (IF 1.431) Pub Date : 2020-01-18
    Hira Taqdees Syeda, Gerwin Klein

    Operating system (OS) kernels achieve isolation between user-level processes using hardware features such as multi-level page tables and translation lookaside buffers (TLBs). The TLB caches address translation, and therefore correctly controlling the TLB is a fundamental security property of OS kernels—yet all large-scale formal OS verification projects we are aware of leave the correct functionality

  • A Library for Formalization of Linear Error-Correcting Codes
    J. Autom. Reason. (IF 1.431) Pub Date : 2020-01-06
    Reynald Affeldt, Jacques Garrigue, Takafumi Saikawa

    Error-correcting codes add redundancy to transmitted data to ensure reliable communication over noisy channels. Since they form the foundations of digital communication, their correctness is a matter of concern. To enable trustful verification of linear error-correcting codes, we have been carrying out a systematic formalization in the Coq proof-assistant. This formalization includes the material that

  • A Relaxation of Üresin and Dubois’ Asynchronous Fixed-Point Theory in Agda
    J. Autom. Reason. (IF 1.431) Pub Date : 2019-12-10
    Matthew L. Daggitt, Ran Zmigrod, Timothy G. Griffin

    Üresin and Dubois’ paper “Parallel Asynchronous Algorithms for Discrete Data” shows how a class of synchronous iterative algorithms may be transformed into asynchronous iterative algorithms. They then prove that the correctness of the resulting asynchronous algorithm can be guaranteed by reasoning about the synchronous algorithm alone. These results have been used to prove the correctness of various

  • Exploring the Structure of an Algebra Text with Locales
    J. Autom. Reason. (IF 1.431) Pub Date : 2019-11-30
    Clemens Ballarin

    Locales, the module system of the theorem prover Isabelle, were designed so that developments in abstract algebra could be represented faithfully and concisely. Whether these goals were met is assessed through a case study. Parts of an algebra textbook, Jacobson’s Basic Algebra, that are challenging structurally were formalised. Key parts of the formalisation are presented in greater detail. An analysis

  • Efficient Strategies for CEGAR-Based Model Checking
    J. Autom. Reason. (IF 1.431) Pub Date : 2019-11-11
    Ákos Hajdu, Zoltán Micskei

    Automated formal verification is often based on the Counterexample-Guided Abstraction Refinement (CEGAR) approach. Many variants of CEGAR have been developed over the years as different problem domains usually require different strategies for efficient verification. This has lead to generic and configurable CEGAR frameworks, which can incorporate various algorithms. In our paper we propose six novel

  • Hammer for Coq: Automation for Dependent Type Theory.
    J. Autom. Reason. (IF 1.431) Pub Date : 2018-08-03
    Łukasz Czajka,Cezary Kaliszyk

    Hammers provide most powerful general purpose automation for proof assistants based on HOL and set theory today. Despite the gaining popularity of the more advanced versions of type theory, such as those based on the Calculus of Inductive Constructions, the construction of hammers for such foundations has been hindered so far by the lack of translation and reconstruction components. In this paper,

  • A Verified SAT Solver Framework with Learn, Forget, Restart, and Incrementality.
    J. Autom. Reason. (IF 1.431) Pub Date : 2018-08-03
    Jasmin Christian Blanchette,Mathias Fleury,Peter Lammich,Christoph Weidenbach

    We developed a formal framework for conflict-driven clause learning (CDCL) using the Isabelle/HOL proof assistant. Through a chain of refinements, an abstract CDCL calculus is connected first to a more concrete calculus, then to a SAT solver expressed in a functional programming language, and finally to a SAT solver in an imperative language, with total correctness guarantees. The framework offers

  • Verified iptables Firewall Analysis and Verification.
    J. Autom. Reason. (IF 1.431) Pub Date : 2018-08-03
    Cornelius Diekmann,Lars Hupel,Julius Michaelis,Maximilian Haslbeck,Georg Carle

    This article summarizes our efforts around the formally verified static analysis of iptables rulesets using Isabelle/HOL. We build our work around a formal semantics of the behavior of iptables firewalls. This semantics is tailored to the specifics of the filter table and supports arbitrary match expressions, even new ones that may be added in the future. Around that, we organize a set of simplification

  • A Verified ODE Solver and the Lorenz Attractor.
    J. Autom. Reason. (IF 1.431) Pub Date : 2018-08-03
    Fabian Immler

    A rigorous numerical algorithm, formally verified with Isabelle/HOL, is used to certify the computations that Tucker used to prove chaos for the Lorenz attractor. The verification is based on a formalization of a diverse variety of mathematics and algorithms. Formalized mathematics include ordinary differential equations and Poincaré maps. Algorithms include low level approximation schemes based on

  • The Role of the Mizar Mathematical Library for Interactive Proof Development in Mizar.
    J. Autom. Reason. (IF 1.431) Pub Date : 2018-08-03
    Grzegorz Bancerek,Czesław Byliński,Adam Grabowski,Artur Korniłowicz,Roman Matuszewski,Adam Naumowicz,Karol Pąk

    The Mizar system is one of the pioneering systems aimed at supporting mathematical proof development on a computer that have laid the groundwork for and eventually have evolved into modern interactive proof assistants. We claim that an important milestone in the development of these systems was the creation of organized libraries accumulating all previously available formalized knowledge in such a

  • OWL Reasoning: Subsumption Test Hardness and Modularity.
    J. Autom. Reason. (IF 1.431) Pub Date : 2018-08-03
    Nicolas Matentzoglu,Bijan Parsia,Uli Sattler

    Reasoning with SROIQ(D) , the logic that underpins the popular Web Ontology Language (OWL), has a high worst case complexity (N2Exptime). Decomposing the ontology into modules prior to classification, and then classifying the composites one-by-one, has been suggested as a way to mitigate this complexity in practice. Modular reasoning is currently motivated by the potential for reducing the hardness

  • Genetic Programming + Proof Search = Automatic Improvement.
    J. Autom. Reason. (IF 1.431) Pub Date : 2018-08-03
    Zoltan A Kocsis,Jerry Swan

    Search Based Software Engineering techniques are emerging as important tools for software maintenance. Foremost among these is Genetic Improvement, which has historically applied the stochastic techniques of Genetic Programming to optimize pre-existing program code. Previous work in this area has not generally preserved program semantics and this article describes an alternative to the traditional

  • Relative Termination via Dependency Pairs.
    J. Autom. Reason. (IF 1.431) Pub Date : 2017-01-01
    José Iborra,Naoki Nishida,Germán Vidal,Akihisa Yamada

    A term rewrite system is terminating when no infinite reduction sequences are possible. Relative termination generalizes termination by permitting infinite reductions as long as some distinguished rules are not applied infinitely many times. Relative termination is thus a fundamental notion that has been used in a number of different contexts, like analyzing the confluence of rewrite systems or the

  • Higher-Order Pattern Anti-Unification in Linear Time.
    J. Autom. Reason. (IF 1.431) Pub Date : 2017-01-01
    Alexander Baumgartner,Temur Kutsia,Jordi Levy,Mateu Villaret

    We present a rule-based Huet's style anti-unification algorithm for simply typed lambda-terms, which computes a least general higher-order pattern generalization. For a pair of arbitrary terms of the same type, such a generalization always exists and is unique modulo α -equivalence and variable renaming. With a minor modification, the algorithm works for untyped lambda-terms as well. The time complexity

  • A Fully Automatic Theorem Prover with Human-Style Output.
    J. Autom. Reason. (IF 1.431) Pub Date : 2017-01-01
    M Ganesalingam,W T Gowers

    This paper describes a program that solves elementary mathematical problems, mostly in metric space theory, and presents solutions that are hard to distinguish from solutions that might be written by human mathematicians.

  • An Approximation Framework for Solvers and Decision Procedures.
    J. Autom. Reason. (IF 1.431) Pub Date : 2017-01-01
    Aleksandar Zeljić,Christoph M Wintersteiger,Philipp Rümmer

    We consider the problem of automatically and efficiently computing models of constraints, in the presence of complex background theories such as floating-point arithmetic. Constructing models, or proving that a constraint is unsatisfiable, has various applications, for instance for automatic generation of test inputs. It is well-known that a naïve encoding of constraints into simpler theories (for

  • The OWL Reasoner Evaluation (ORE) 2015 Competition Report.
    J. Autom. Reason. (IF 1.431) Pub Date : 2017-01-01
    Bijan Parsia,Nicolas Matentzoglu,Rafael S Gonçalves,Birte Glimm,Andreas Steigmiller

    The OWL Reasoner Evaluation competition is an annual competition (with an associated workshop) that pits OWL 2 compliant reasoners against each other on various standard reasoning tasks over naturally occurring problems. The 2015 competition was the third of its sort and had 14 reasoners competing in six tracks comprising three tasks (consistency, classification, and realisation) over two profiles

  • Complexity and Resource Bound Analysis of Imperative Programs Using Difference Constraints.
    J. Autom. Reason. (IF 1.431) Pub Date : 2017-01-01
    Moritz Sinn,Florian Zuleger,Helmut Veith

    Difference constraints have been used for termination analysis in the literature, where they denote relational inequalities of the form x'≤y+c , and describe that the value of x in the current state is at most the value of y in the previous state plus some constant c∈Z . We believe that difference constraints are also a good choice for complexity and resource bound analysis because the complexity of

  • A Formal C Memory Model for Separation Logic.
    J. Autom. Reason. (IF 1.431) Pub Date : 2016-01-01
    Robbert Krebbers

    The core of a formal semantics of an imperative programming language is a memory model that describes the behavior of operations on the memory. Defining a memory model that matches the description of C in the C11 standard is challenging because C allows both high-level (by means of typed expressions) and low-level (by means of bit manipulation) memory accesses. The C11 standard has restricted the interaction

  • Labelled Interpolation Systems for Hyper-Resolution, Clausal, and Local Proofs.
    J. Autom. Reason. (IF 1.431) Pub Date : 2016-01-01
    Matthias Schlaipfer,Georg Weissenbacher

    Craig's interpolation theorem has numerous applications in model checking, automated reasoning, and synthesis. There is a variety of interpolation systems which derive interpolants from refutation proofs; these systems are ad-hoc and rigid in the sense that they provide exactly one interpolant for a given proof. In previous work, we introduced a parametrised interpolation system which subsumes existing

  • On Definitions of Constants and Types in HOL.
    J. Autom. Reason. (IF 1.431) Pub Date : 2016-01-01
    Rob Arthan

    This paper reports on a simpler and more powerful replacement for the principles for defining new constants that were previously provided in the various HOL implementations. We discuss the problems that the new principle is intended to solve and sketch the proofs that it is conservative and that it subsumes the earlier definitional principles. The new definitional principle for constants has been implemented

  • The Higher-Order Prover Leo-II.
    J. Autom. Reason. (IF 1.431) Pub Date : 2015-01-01
    Christoph Benzmüller,Nik Sultana,Lawrence C Paulson,Frank Theiß

    Leo-II is an automated theorem prover for classical higher-order logic. The prover has pioneered cooperative higher-order-first-order proof automation, it has influenced the development of the TPTP THF infrastructure for higher-order logic, and it has been applied in a wide array of problems. Leo-II may also be called in proof assistants as an external aid tool to save user effort. For this it is crucial

  • Reinterpreting Dependency Schemes: Soundness Meets Incompleteness in DQBF.
    J. Autom. Reason. (IF 1.431) Pub Date : null
    Olaf Beyersdorff,Joshua Blinkhorn,Leroy Chew,Renate Schmidt,Martin Suda

    Dependency quantified Boolean formulas (DQBF) and QBF dependency schemes have been treated separately in the literature, even though both treatments extend QBF by replacing the linear order of the quantifier prefix with a partial order. We propose to merge the two, by reinterpreting a dependency scheme as a mapping from QBF into DQBF. Our approach offers a fresh insight on the nature of soundness in

  • Long-Distance Q-Resolution with Dependency Schemes.
    J. Autom. Reason. (IF 1.431) Pub Date : null
    Tomáš Peitl,Friedrich Slivovsky,Stefan Szeider

    Resolution proof systems for quantified Boolean formulas (QBFs) provide a formal model for studying the limitations of state-of-the-art search-based QBF solvers that use these systems to generate proofs. We study a combination of two proof systems supported by the solver DepQBF: Q-resolution with generalized universal reduction according to a dependency scheme and long distance Q-resolution. We show

  • Verifying OpenJDK's Sort Method for Generic Collections.
    J. Autom. Reason. (IF 1.431) Pub Date : null
    Stijn de Gouw,Frank S de Boer,Richard Bubel,Reiner Hähnle,Jurriaan Rot,Dominic Steinhöfel

    TimSort is the main sorting algorithm provided by the Java standard library and many other programming frameworks. Our original goal was functional verification of TimSort with mechanical proofs. However, during our verification attempt we discovered a bug which causes the implementation to crash by an uncaught exception. In this paper, we identify conditions under which the bug occurs, and from this

  • Extraction of Expansion Trees.
    J. Autom. Reason. (IF 1.431) Pub Date : null
    Alexander Leitsch,Anela Lolic

    We define a new method for proof mining by CERES (cut-elimination by resolution) that is concerned with the extraction of expansion trees in first-order logic (see Miller in Stud Log 46(4):347-370, 1987) with equality. In the original CERES method expansion trees can be extracted from proofs in normal form (proofs without quantified cuts) as a post-processing of cut-elimination. More precisely they

  • An Assertional Proof of Red–Black Trees Using Dafny
    J. Autom. Reason. (IF 1.431) Pub Date : 2019-10-03
    Ricardo Peña

    Red–black trees are convenient data structures for inserting, searching, and deleting keys with logarithmic costs. However, keeping them balanced requires careful programming, and sometimes to deal with a high number of cases. In this paper, we present a functional version of a red–black tree variant called left-leaning, due to R. Sedgewick, which reduces the number of cases to be dealt with to a few

  • First-Order Automated Reasoning with Theories: When Deduction Modulo Theory Meets Practice
    J. Autom. Reason. (IF 1.431) Pub Date : 2019-09-23
    Guillaume Burel, Guillaume Bury, Raphaël Cauderlier, David Delahaye, Pierre Halmagrand, Olivier Hermant

    We discuss the practical results obtained by the first generation of automated theorem provers based on Deduction modulo theory. In particular, we demonstrate the concrete improvements such a framework can bring to first-order theorem provers with the introduction of a rewrite feature. Deduction modulo theory is an extension of predicate calculus with rewriting both on terms and propositions. It is

  • Automatically Verifying Temporal Properties of Pointer Programs with Cyclic Proof
    J. Autom. Reason. (IF 1.431) Pub Date : 2019-08-09
    Gadi Tellez, James Brotherston

    In this article, we investigate the automated verification of temporal properties of heap-aware programs. We propose a deductive reasoning approach based on cyclic proof. Judgements in our proof system assert that a program has a certain temporal property over memory state assertions, written in separation logic with user-defined inductive predicates, while the proof rules of the system unfold temporal

  • Formalizing the Cox–Ross–Rubinstein Pricing of European Derivatives in Isabelle/HOL
    J. Autom. Reason. (IF 1.431) Pub Date : 2019-07-04
    Mnacho Echenim, Hervé Guiol, Nicolas Peltier

    We formalize in the proof assistant Isabelle essential basic notions and results in financial mathematics. We provide generic formal definitions of concepts such as markets, portfolios, derivative products, arbitrages or fair prices, and we show that, under the usual no-arbitrage condition, the existence of a replicating portfolio for a derivative implies that the latter admits a unique fair price

  • A Verified Implementation of the Berlekamp–Zassenhaus Factorization Algorithm
    J. Autom. Reason. (IF 1.431) Pub Date : 2019-06-17
    Jose Divasón, Sebastiaan J. C. Joosten, René Thiemann, Akihisa Yamada

    We formally verify the Berlekamp–Zassenhaus algorithm for factoring square-free integer polynomials in Isabelle/HOL. We further adapt an existing formalization of Yun’s square-free factorization algorithm to integer polynomials, and thus provide an efficient and certified factorization algorithm for arbitrary univariate polynomials. The algorithm first performs factorization in the prime field \(\mathrm

  • Efficient Verified (UN)SAT Certificate Checking
    J. Autom. Reason. (IF 1.431) Pub Date : 2019-06-04
    Peter Lammich

    SAT solvers decide the satisfiability of Boolean formulas in conjunctive normal form. They are commonly used for software and hardware verification. Modern SAT solvers are highly complex and optimized programs. As a single bug in the solver may invalidate the verification of many systems, SAT solvers output certificates for their answer, which are then checked independently. However, even certificate

  • Automated Reasoning with Power Maps
    J. Autom. Reason. (IF 1.431) Pub Date : 2019-05-07
    G. I. Moghaddam, R. Padmanabhan, Yang Zhang

    In this paper, we employ automated deduction techniques to prove and generalize some well-known theorems in group theory that involve power maps \( x^n\). The difficulty lies in the fact that the term \(x^n\) cannot be expressed in the syntax of first-order logic when n is an integer variable. Here we employ a new concept of “power-like functions” by extracting relevant equational properties valid

  • Homogeneous Length Functions on Groups: Intertwined Computer and Human Proofs
    J. Autom. Reason. (IF 1.431) Pub Date : 2019-04-16
    Siddhartha Gadgil

    We describe a case of an interplay between human and computer proving which played a role in the discovery of an interesting mathematical result (Fritz et al. in Algebra Number Theory 12:1773–1786, 2018). The unusual feature of the use of computers here was that a computer generated but human readable proof was read, understood, generalized and abstracted by mathematicians to obtain the key lemma in

  • A Formalized General Theory of Syntax with Bindings: Extended Version
    J. Autom. Reason. (IF 1.431) Pub Date : 2019-04-16
    Lorenzo Gheri, Andrei Popescu

    We present the formalization of a theory of syntax with bindings that has been developed and refined over the last decade to support several large formalization efforts. Terms are defined for an arbitrary number of constructors of varying numbers of inputs, quotiented to alpha-equivalence and sorted according to a binding signature. The theory contains a rich collection of properties of the standard

  • Strong Extension-Free Proof Systems
    J. Autom. Reason. (IF 1.431) Pub Date : 2019-02-22
    Marijn J. H. Heule, Benjamin Kiesl, Armin Biere

    We introduce proof systems for propositional logic that admit short proofs of hard formulas as well as the succinct expression of most techniques used by modern SAT solvers. Our proof systems allow the derivation of clauses that are not necessarily implied, but which are redundant in the sense that their addition preserves satisfiability. To guarantee that these added clauses are redundant, we consider

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