scholarly journals Temporal prophecy for proving temporal properties of infinite-state systems

2021 ◽  
Author(s):  
Oded Padon ◽  
Jochen Hoenicke ◽  
Kenneth L. McMillan ◽  
Andreas Podelski ◽  
Mooly Sagiv ◽  
...  
Keyword(s):  
Order Logic ◽  
Cut Elimination ◽  
Temporal Property ◽  
Deductive Verification ◽  
First Order ◽  
Temporal Properties ◽  
Safety Property ◽  
Infinite State Systems ◽  
Verification Techniques ◽  
Infinite State

AbstractVarious verification techniques for temporal properties transform temporal verification to safety verification. For infinite-state systems, these transformations are inherently imprecise. That is, for some instances, the temporal property holds, but the resulting safety property does not. This paper introduces a mechanism for tackling this imprecision. This mechanism, which we call temporal prophecy, is inspired by prophecy variables. Temporal prophecy refines an infinite-state system using first-order linear temporal logic formulas, via a suitable tableau construction. For a specific liveness-to-safety transformation based on first-order logic, we show that using temporal prophecy strictly increases the precision. Furthermore, temporal prophecy leads to robustness of the proof method, which is manifested by a cut elimination theorem. We integrate our approach into the Ivy deductive verification system, and show that it can handle challenging temporal verification examples.

AUTOMATED TERMINATION IN MODEL-CHECKING MODULO THEORIES

2013 ◽  
Vol 24 (02) ◽  
pp. 211-232 ◽  
Author(s):  
ALESSANDRO CARIONI ◽  
SILVIO GHILARDI ◽  
SILVIO RANISE
Keyword(s):  
Model Checking ◽  
Sufficient Conditions ◽  
Order Logic ◽  
Satisfiability Modulo Theories ◽  
First Order Logic ◽  
Reachability Problem ◽  
First Order ◽  
Recent Advances ◽  
Infinite State Systems ◽  
Infinite State

We identify sufficient conditions to automatically establish the termination of a backward reachability procedure for infinite state systems by using well-quasi-orderings. Besides showing that backward reachability succeeds on many instances of problems covered by general termination results, we argue that it could predict termination also on interesting instances of the reachability problem that are outside the scope of applicability of such general results. We work in the declarative framework of Model Checking Modulo Theories that permits us to exploit recent advances in Satisfiability Modulo Theories solving and model-theoretic notions of first-order logic.

scholarly journals Sound Verification Procedures for Temporal Properties of Infinite-State Systems

2021 ◽  
pp. 337-360
Author(s):  
Quentin Peyras ◽  
Jean-Paul Bodeveix ◽  
Julien Brunel ◽  
David Chemouil
Keyword(s):  
Distributed Systems ◽  
State Space ◽  
Temporal Logic ◽  
Order Linear ◽  
First Order ◽  
Temporal Properties ◽  
Liveness Properties ◽  
Infinite State Systems ◽  
High Degree ◽  
Infinite State

AbstractFirst-Order Linear Temporal Logic (FOLTL) is particularly convenient to specify distributed systems, in particular because of the unbounded aspect of their state space. We have recently exhibited novel decidable fragments of FOLTL which pave the way for tractable verification. However, these fragments are not expressive enough for realistic specifications. In this paper, we propose three transformations to translate a typical FOLTL specification into two of its decidable fragments. All three transformations are proved sound (the associated propositions are proved in Coq) and have a high degree of automation. To put these techniques into practice, we propose a specification language relying on FOLTL, as well as a prototype which performs the verification, relying on existing model checkers. This approach allows us to successfully verify safety and liveness properties for various specifications of distributed systems from the literature.

scholarly journals Model Completeness, Uniform Interpolants and Superposition Calculus

2021 ◽  
Author(s):  
Diego Calvanese ◽  
Silvio Ghilardi ◽  
Alessandro Gianola ◽  
Marco Montali ◽  
Andrey Rivkin
Keyword(s):  
Automated Reasoning ◽  
Quantifier Elimination ◽  
Effective Solution ◽  
Model Completeness ◽  
Present Contribution ◽  
First Order ◽  
Reduction Strategies ◽  
Infinite State Systems ◽  
Infinite State ◽  
Superposition Calculus

AbstractUniform interpolants have been largely studied in non-classical propositional logics since the nineties; a successive research line within the automated reasoning community investigated uniform quantifier-free interpolants (sometimes referred to as “covers”) in first-order theories. This further research line is motivated by the fact that uniform interpolants offer an effective solution to tackle quantifier elimination and symbol elimination problems, which are central in model checking infinite state systems. This was first pointed out in ESOP 2008 by Gulwani and Musuvathi, and then by the authors of the present contribution in the context of recent applications to the verification of data-aware processes. In this paper, we show how covers are strictly related to model completions, a well-known topic in model theory. We also investigate the computation of covers within the Superposition Calculus, by adopting a constrained version of the calculus and by defining appropriate settings and reduction strategies. In addition, we show that computing covers is computationally tractable for the fragment of the language used when tackling the verification of data-aware processes. This observation is confirmed by analyzing the preliminary results obtained using the mcmt tool to verify relevant examples of data-aware processes. These examples can be found in the last version of the tool distribution.

A proof-theoretic treatment of λ-reduction with cut-elimination: λ-calculus as a logic programming language

2011 ◽  
Vol 76 (2) ◽  
pp. 673-699 ◽  
Author(s):  
Michael Gabbay
Keyword(s):  
Logic Programming ◽  
Programming Language ◽  
Functional Programming ◽  
Order Logic ◽  
First Order Logic ◽  
Cut Elimination ◽  
Logic Programming Language ◽  
First Order ◽  
Functional Programming Language ◽  
Sequent System

AbstractWe build on an existing a term-sequent logic for the λ-calculus. We formulate a general sequent system that fully integrates αβη-reductions between untyped λ-terms into first order logic.We prove a cut-elimination result and then offer an application of cut-elimination by giving a notion of uniform proof for λ-terms. We suggest how this allows us to view the calculus of untyped αβ-reductions as a logic programming language (as well as a functional programming language, as it is traditionally seen).

scholarly journals Generalization strategies for the verification of infinite state systems

2012 ◽  
Vol 13 (2) ◽  
pp. 175-199 ◽  
Author(s):  
FABIO FIORAVANTI ◽  
ALBERTO PETTOROSSI ◽  
MAURIZIO PROIETTI ◽  
VALERIO SENNI
Keyword(s):  
Program Analysis ◽  
Second Phase ◽  
Initial State ◽  
Verification Method ◽  
Program Specialization ◽  
Temporal Properties ◽  
Infinite State Systems ◽  
Two Phases ◽  
Constraint Logic Programs ◽  
Infinite State

AbstractWe present a method for the automated verification of temporal properties of infinite state systems. Our verification method is based on the specialization of constraint logic programs (CLP) and works in two phases: (1) in the first phase, a CLP specification of an infinite state system is specialized with respect to the initial state of the system and the temporal property to be verified, and (2) in the second phase, the specialized program is evaluated by using a bottom-up strategy. The effectiveness of the method strongly depends on the generalization strategy which is applied during the program specialization phase. We consider several generalization strategies obtained by combining techniques already known in the field of program analysis and program transformation, and we also introduce some new strategies. Then, through many verification experiments, we evaluate the effectiveness of the generalization strategies we have considered. Finally, we compare the implementation of our specialization-based verification method to other constraint-based model checking tools. The experimental results show that our method is competitive with the methods used by those other tools.

scholarly journals Sharpened lower bounds for cut elimination

2012 ◽  
Vol 77 (2) ◽  
pp. 656-668
Author(s):  
Samuel R. Buss
Keyword(s):  
Lower Bounds ◽  
Order Logic ◽  
Maximum Depth ◽  
First Order Logic ◽  
Cut Elimination ◽  
Original Proof ◽  
First Order

AbstractWe present sharpened lower bounds on the size of cut free proofs for first-order logic. Prior lower bounds for eliminating cuts from a proof established superexponential lower bounds as a stack of exponentials, with the height of the stack proportional to the maximum depthdof the formulas in the original proof. Our results remove the constant of proportionality, giving an exponential stack of height equal tod−O(1). The proof method is based on more efficiently expressing the Gentzen–Solovay cut formulas as low depth formulas.

scholarly journals Verification of Temporal Properties of Concurrent Systems

1993 ◽  
Vol 22 (445) ◽  
Author(s):  
Henrik Reif Andersen
Keyword(s):  
Model Checking ◽  
Concurrent Systems ◽  
Temporal Properties ◽  
Compositional Approach ◽  
Completeness Result ◽  
Finite State ◽  
Infinite State Systems ◽  
Novel Applications ◽  
Infinite State ◽  
Intuitionistic Version

This thesis is concerned with the verification of concurrent systems modelled by process algebras. It provides methods and techniques for reasoning about temporal properties as described by assertions from an expressive modal logic -- the modal µ-calculus. It describes a compositional approach to model checking, efficient local and global algorithms for model checking finite-state systems, a general local fixed-point finding algorithm, a proof system for model checking infinite-state systems, a categorical completeness result for an intuitionistic version of the modal µ-calculus, and finally it shows some novel applications of the logic for expressing behavioural relations.

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