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2022 ◽  
Vol 6 (POPL) ◽  
pp. 1-29
Author(s):  
Takeshi Tsukada ◽  
Hiroshi Unno

This paper shows that a variety of software model-checking algorithms can be seen as proof-search strategies for a non-standard proof system, known as a cyclic proof system . Our use of the cyclic proof system as a logical foundation of software model checking enables us to compare different algorithms, to reconstruct well-known algorithms from a few simple principles, and to obtain soundness proofs of algorithms for free. Among others, we show the significance of a heuristics based on a notion that we call maximal conservativity ; this explains the cores of important algorithms such as property-directed reachability (PDR) and reveals a surprising connection to an efficient solver of games over infinite graphs that was not regarded as a kind of PDR.


Author(s):  
Wilfried Sieg ◽  
Farzaneh Derakhshan
Keyword(s):  

2021 ◽  
pp. 103026
Author(s):  
José Espírito Santo ◽  
Ralph Matthes ◽  
Luís Pinto
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Author(s):  
Peter Backeman ◽  
Philipp Rümmer ◽  
Aleksandar Zeljić

AbstractThe inference of program invariants over machine arithmetic, commonly called bit-vector arithmetic, is an important problem in verification. Techniques that have been successful for unbounded arithmetic, in particular Craig interpolation, have turned out to be difficult to generalise to machine arithmetic: existing bit-vector interpolation approaches are based either on eager translation from bit-vectors to unbounded arithmetic, resulting in complicated constraints that are hard to solve and interpolate, or on bit-blasting to propositional logic, in the process losing all arithmetic structure. We present a new approach to bit-vector interpolation, as well as bit-vector quantifier elimination (QE), that works by lazy translation of bit-vector constraints to unbounded arithmetic. Laziness enables us to fully utilise the information available during proof search (implied by decisions and propagation) in the encoding, and this way produce constraints that can be handled relatively easily by existing interpolation and QE procedures for Presburger arithmetic. The lazy encoding is complemented with a set of native proof rules for bit-vector equations and non-linear (polynomial) constraints, this way minimising the number of cases a solver has to consider. We also incorporate a method for handling concatenations and extractions of bit-vector efficiently.


2021 ◽  
Vol 14 (2) ◽  
pp. 215-229
Author(s):  
Tiziano Dalmonte ◽  
Sara Negri ◽  
Nicola Olivetti ◽  
Gian Luca Pozzato

In this work we present PRONOM, a theorem prover and countermodel generator for non-normal modal logics. PRONOM implements some labelled sequent calculi recently introduced for the basic system E and its extensions with axioms M, N, and C based on bi-neighbourhood semantics. PRONOM is inspired by the methodology of leanTAP and is implemented in Prolog. When a modal formula is valid, then PRONOM computes a proof (a closed tree) in the labelled calculi having a sequent with an empty left-hand side and containing only that formula on the right-hand side as a root, otherwise PRONOM is able to extract a model falsifying it from an open, saturated branch. The paper shows some experimental results, witnessing that the performances of PRONOM are promising.


Author(s):  
Camillo Fiorentini

AbstractWe present an efficient proof search procedure for Intuitionistic Propositional Logic which involves the use of an incremental SAT-solver. Basically, it is obtained by adding a restart operation to the system by Claessen and Rosén, thus we call our implementation . We gain some remarkable advantages: derivations have a simple structure; countermodels are in general small; using a standard benchmarks suite, we outperform and other state-of-the-art provers.


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