• J. Autom. Reason. (IF 1.431) Pub Date : 2020-10-21
Véronique Cortier, Stéphanie Delaune, Vaishnavi Sundararajan

We identify a new decidable class of security protocols, both for reachability and equivalence properties. Our result holds for an unbounded number of sessions and for protocols with nonces. It covers all standard cryptographic primitives. Our class sets up three main assumptions. (i) Protocols need to be “simple”, meaning that an attacker can precisely identify from which participant and which session

更新日期：2020-10-26
• J. Autom. Reason. (IF 1.431) Pub Date : 2020-09-14
Guillaume Ambal, Sergueï Lenglet, Alan Schmitt

We present a formalization of HO$$\pi$$ in Coq, a process calculus where messages carry processes. Such a higher-order calculus features two very different kinds of binder: process input, similar to $$\lambda$$-abstraction, and name restriction, whose scope can be expanded by communication. For the latter, we compare four approaches to represent binders: locally nameless, de Bruijn indices, nominal

更新日期：2020-09-14
• J. Autom. Reason. (IF 1.431) Pub Date : 2020-09-09
D. Butler, A. Lochbihler, D. Aspinall, A. Gascón

Machine-checked proofs of security are important to increase the rigour of provable security. In this work we present a formalised theory of two fundamental two party cryptographic primitives: $$\varSigma$$-protocols and Commitment Schemes. $$\varSigma$$-protocols allow a prover to convince a verifier that they possess some knowledge without leaking information about the knowledge. Commitment schemes

更新日期：2020-09-10
• J. Autom. Reason. (IF 1.431) Pub Date : 2020-09-05
Michael Färber, Cezary Kaliszyk, Josef Urban

Connection calculi allow for very compact implementations of goal-directed proof search. We give an overview of our work related to connection tableaux calculi: first, we show optimised functional implementations of connection tableaux proof search, including a consistent Skolemisation procedure for machine learning. Then, we show two guidance methods based on machine learning, namely reordering of

更新日期：2020-09-06
• J. Autom. Reason. (IF 1.431) Pub Date : 2020-09-02
Hing Lun Chan, Michael Norrish

The AKS algorithm (by Agrawal, Kayal and Saxena) is a significant theoretical result, establishing “PRIMES in P” by a brilliant application of ideas from finite fields. This paper describes an implementation of the AKS algorithm in our theorem prover HOL4, together with a proof of its correctness and its computational complexity. The complexity analysis is based on a conservative computation model

更新日期：2020-09-02
• J. Autom. Reason. (IF 1.431) Pub Date : 2020-08-29
Kshitij Bansal, Eric Koskinen, Omer Tripp

Reasoning about commutativity between data-structure operations is an important problem with many applications. In the sequential setting, commutativity can be used to reason about the correctness of refactoring, compiler transformations, and identify instances of non-determinism. In parallel contexts, commutativity dates back to the database (Weihl in IEEE Trans Comput 37(12):1488–1505, 1988) and

更新日期：2020-08-29
• J. Autom. Reason. (IF 1.431) Pub Date : 2020-08-29
Silvio Ghilardi, Elena Pagani

We develop quantifier elimination procedures for fragments of higher order logic arising from the formalization of distributed systems (especially of fault-tolerant ones). Such procedures can be used in symbolic manipulations like the computation of pre/post images and of projections. We show in particular that our procedures are quite effective in producing counter abstractions that can be model-checked

更新日期：2020-08-29
• J. Autom. Reason. (IF 1.431) Pub Date : 2020-08-20
Thibault Gauthier, Cezary Kaliszyk, Josef Urban, Ramana Kumar, Michael Norrish

We implement an automated tactical prover TacticToe on top of the HOL4 interactive theorem prover. TacticToe learns from human proofs which mathematical technique is suitable in each proof situation. This knowledge is then used in a Monte Carlo tree search algorithm to explore promising tactic-level proof paths. On a single CPU, with a time limit of 60 s, TacticToe proves 66.4% of the 7164 theorems

更新日期：2020-08-20
• J. Autom. Reason. (IF 1.431) Pub Date : 2020-08-14
Zhé Hóu, David Sanan, Alwen Tiu, Yang Liu, Koh Chuen Hoa, Jin Song Dong

The SPARC instruction set architecture (ISA) has been used in various processors in workstations, embedded systems, and in mission-critical industries such as aviation and space engineering. Hence, it is important to provide formal frameworks that facilitate the verification of hardware and software that run on or interface with these processors. In this work, we give the first formal model for multi-core

更新日期：2020-08-14
• J. Autom. Reason. (IF 1.431) Pub Date : 2020-08-13
Gabriele Costa, Letterio Galletta, Pierpaolo Degano, David Basin, Chiara Bodei

Verifying the correctness of a system as a whole requires establishing that it satisfies a global specification. When it does not, it would be helpful to determine which modules are incorrect. As a consequence, specification decomposition is a relevant problem from both a theoretical and practical point of view. Until now, specification decomposition has been independently addressed by the control

更新日期：2020-08-14
• 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

更新日期：2020-08-01
• 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

更新日期：2020-07-31
• 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

更新日期：2020-07-29
• 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

更新日期：2020-07-27
• 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

更新日期：2020-07-21
• 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

更新日期：2020-07-18
• 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

更新日期：2020-07-16
• 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

更新日期：2020-07-14
• J. Autom. Reason. (IF 1.431) Pub Date : 2020-07-13

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

更新日期：2020-07-13
• 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

更新日期：2020-06-27
• 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

更新日期：2020-06-24
• 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

更新日期：2020-06-18
• 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

更新日期：2020-06-09
• 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

更新日期：2020-06-06
• 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

更新日期：2020-06-06
• 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

更新日期：2020-05-29
• 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

更新日期：2020-05-22
• 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

更新日期：2020-05-22
• 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.

更新日期：2020-04-30
• 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

更新日期：2020-03-06
• 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

更新日期：2020-02-25
• 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

更新日期：2020-02-19
• J. Autom. Reason. (IF 1.431) Pub Date : 2020-02-18
Matthieu Sozeau; Abhishek Anand; Simon Boulier; Cyril Cohen; Yannick Forster; Fabian Kunze; Gregory Malecha; Nicolas Tabareau; Théo Winterhalter

The MetaCoq project aims to provide a certified meta-programming environment in Coq. It builds on Template-Coq, a plugin for Coq originally implemented by Malecha (Extensible proof engineering in intensional type theory, Harvard University, http://gmalecha.github.io/publication/2015/02/01/extensible-proof-engineering-in-intensional-type-theory.html, 2014), which provided a reifier for Coq terms and

更新日期：2020-02-18
• J. Autom. Reason. (IF 1.431) Pub Date : 2020-02-17
Gilles Barthe, Gustavo Betarte, Juan Diego Campo, Carlos Luna, David Pichardie

This paper constitutes the second part of a paper published in Barthe et al. (J Autom Reason, 2017. https://doi.org/10.1007/s10817-017-9441-5). Cache-based attacks are a class of side-channel attacks that are particularly effective in virtualized or cloud-based environments, where they have been used to recover secret keys from cryptographic implementations. One common approach to thwart cache-based

更新日期：2020-02-17
• J. Autom. Reason. (IF 1.431) Pub Date : 2020-02-13
R. Alonderis, R. Pliuškevičius, A. Pliuškevičienė, H. Giedra

Various types of calculi (Hilbert, Gentzen sequent, resolution calculi, tableaux) for propositional linear temporal logic (PLTL) have been invented. In this paper, a sound and complete loop-type sequent calculus $$\mathbf{G} _\text {L}{} \mathbf{T}$$ for PLTL with the temporal operators “next” and “henceforth always” ($${\mathbf{PLTL}}^{n,a}$$) is considered at first. We prove that all rules of $$\mathbf{G} 更新日期：2020-02-13 • 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 更新日期：2020-02-08 • 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. 更新日期：2020-01-31 • 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 更新日期：2020-01-18 • J. Autom. Reason. (IF 1.431) Pub Date : 2020-01-16 Salvador Lucas, José Meseguer, Raúl Gutiérrez Proving termination of programs in ‘real-life’ rewriting-based languages like CafeOBJ, Haskell, Maude, etc., is an important subject of research. To advance this goal, faithfully capturing the impact in the termination behavior of the main language features (e.g., conditions in program rules) is essential. In Part I of this work, we have introduced a 2D Dependency Pair Framework for automatically proving 更新日期：2020-01-16 • 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 更新日期：2020-01-06 • 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 更新日期：2019-12-10 • 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 更新日期：2019-11-30 • 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 更新日期：2019-11-11 • 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 更新日期：2019-10-03 • 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 更新日期：2019-09-23 • 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 更新日期：2019-08-09 • J. Autom. Reason. (IF 1.431) Pub Date : 2019-07-31 Patrick Baillot; Gilles Barthe; Ugo Dal Lago We define a call-by-value variant of Gödel’s system \(\textsf {T}$$ with references, and equip it with a linear dependent type and effect system, called $$\textsf {d}\ell \textsf {T}$$, that can estimate the time complexity of programs, as a function of the size of their inputs. We prove that the type system is intentionally sound, in the sense that it over-approximates the complexity of executing

更新日期：2019-07-31
• 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

更新日期：2019-07-04
• J. Autom. Reason. (IF 1.431) Pub Date : 2019-06-22
Mohamed Yousri Mahmoud; Amy P. Felty

We develop a linear logical framework within the Hybrid system and use it to reason about the type system of a quantum lambda calculus. In particular, we consider a practical version of the calculus called Proto-Quipper, which contains the core of Quipper. Quipper is a quantum programming language under active development and recently has gained much popularity among the quantum computing communities

更新日期：2019-06-22
• 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 更新日期：2019-06-17 • 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 更新日期：2019-06-04 • 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

更新日期：2019-05-07
• J. Autom. Reason. (IF 1.431) Pub Date : 2019-04-16

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

更新日期：2019-04-16
• 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

更新日期：2019-04-16
• J. Autom. Reason. (IF 1.431) Pub Date : 2019-04-08
Maximiliano Cristiá; Gianfranco Rossi

In this paper we present a solver for a first-order logic language where sets and binary relations can be freely and naturally combined. The language can express, at least, any full set relation algebra on finite sets. It provides untyped, hereditarily finite sets, whose elements can be variables, and basically all the classic set and relational operators used in formal languages such as B and Z. Sets

更新日期：2019-04-08
• J. Autom. Reason. (IF 1.431) Pub Date : 2019-04-03
Wenda Li; Lawrence C. Paulson

In complex analysis, the winding number measures the number of times a path (counter-clockwise) winds around a point, while the Cauchy index can approximate how the path winds. We formalise this approximation in the Isabelle theorem prover, and provide a tactic to evaluate winding numbers through Cauchy indices. By further combining this approximation with the argument principle, we are able to make

更新日期：2019-04-03
• J. Autom. Reason. (IF 1.431) Pub Date : 2019-03-28
M. Echenim; N. Peltier

A method is devised to integrate reasoning by mathematical induction into saturation-based proof procedures based on resolution or superposition. The obtained calculi are capable of handling formulas in which some of the quantified variables range over inductively defined domains (which, as is well-known, cannot be expressed in first-order logic). The procedure is defined as a set of inference rules

更新日期：2019-03-28
• J. Autom. Reason. (IF 1.431) Pub Date : 2019-03-13
Luca Paolini; Mauro Piccolo; Margherita Zorzi

qPCF is a paradigmatic quantum programming language that extends PCF with quantum circuits and a quantum co-processor. Quantum circuits are treated as classical data that can be duplicated and manipulated in flexible ways by means of a dependent type system. The co-processor is essentially a standard QRAM device, albeit we avoid to store permanently quantum states in between two co-processor’s calls

更新日期：2019-03-13
• J. Autom. Reason. (IF 1.431) Pub Date : 2019-03-01
Peter Baumgartner; Renate A. Schmidt

Model generation is a problem complementary to theorem proving and is important for fault analysis and debugging of formal specifications of security protocols, programs and terminological definitions, for example. This paper discusses several ways of enhancing the paradigm of bottom-up model generation, with the two main contributions being a new range-restriction transformation and generalized blocking

更新日期：2019-03-01
• 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

更新日期：2019-02-22
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