arXiv subjects

Fabio Fioravanti

Publications and source records attributed to Fabio Fioravanti.

25 records · Page 2Linked to original sources

arXiv2016

Removing Unnecessary Variables from Horn Clause Verification Conditions

Verification conditions (VCs) are logical formulas whose satisfiability guarantees program correctness. We consider VCs in the form of constrained Horn clauses (CHC) which are automatically generated from the encoding of (an interpreter of) the operational semantics of the programming language. VCs are derived through program specialization based on the unfold/fold transformation rules and, as it often happens when specializing interpreters, they contain unnecessary variables, that is, variables which are not required for the correctness proofs of the programs under verification. In this paper we adapt to the CHC setting some of the techniques that were developed for removing unnecessary variables from logic programs, and we show that, in some cases, the application of these techniques increases the effectiveness of Horn clause solvers when proving program correctness.

cs.LO↗

arXiv2015

Proving Correctness of Imperative Programs by Linearizing Constrained Horn Clauses

We present a method for verifying the correctness of imperative programs which is based on the automated transformation of their specifications. Given a program prog, we consider a partial correctness specification of the form $\{φ\}$ prog $\{ψ\}$, where the assertions $φ$ and $ψ$ are predicates defined by a set Spec of possibly recursive Horn clauses with linear arithmetic (LA) constraints in their premise (also called constrained Horn clauses). The verification method consists in constructing a set PC of constrained Horn clauses whose satisfiability implies that $\{φ\}$ prog $\{ψ\}$ is valid. We highlight some limitations of state-of-the-art constrained Horn clause solving methods, here called LA-solving methods, which prove the satisfiability of the clauses by looking for linear arithmetic interpretations of the predicates. In particular, we prove that there exist some specifications that cannot be proved valid by any of those LA-solving methods. These specifications require the proof of satisfiability of a set PC of constrained Horn clauses that contain nonlinear clauses (that is, clauses with more than one atom in their premise). Then, we present a transformation, called linearization, that converts PC into a set of linear clauses (that is, clauses with at most one atom in their premise). We show that several specifications that could not be proved valid by LA-solving methods, can be proved valid after linearization. We also present a strategy for performing linearization in an automatic way and we report on some experimental results obtained by using a preliminary implementation of our method.

cs.LO↗

arXiv2014

Verification of Programs by Combining Iterated Specialization with Interpolation

We present a verification technique for program safety that combines Iterated Specialization and Interpolating Horn Clause Solving. Our new method composes together these two techniques in a modular way by exploiting the common Horn Clause representation of the verification problem. The Iterated Specialization verifier transforms an initial set of verification conditions by using unfold/fold equivalence preserving transformation rules. During transformation, program invariants are discovered by applying widening operators. Then the output set of specialized verification conditions is analyzed by an Interpolating Horn Clause solver, hence adding the effect of interpolation to the effect of widening. The specialization and interpolation phases can be iterated, and also combined with other transformations that change the direction of propagation of the constraints (forward from the program preconditions or backward from the error conditions). We have implemented our verification technique by integrating the VeriMAP verifier with the FTCLP Horn Clause solver, based on Iterated Specialization and Interpolation, respectively. Our experimental results show that the integrated verifier improves the precision of each of the individual components run separately.

cs.LO↗

arXiv2014

Proceedings First Workshop on Horn Clauses for Verification and Synthesis

This volume contains the proceedings of HCVS 2014, the First Workshop on Horn Clauses for Verification and Synthesis which was held on July 17, 2014 in Vienna, Austria as a satellite event of the Federated Logic Conference (FLoC) and part of the Vienna Summer of Logic (VSL 2014). HCVS 2014 was affiliated to the 26th International Conference on Computer Aided Verification (CAV 2014) and to the 30th International Conference on Logic Programming (ICLP 2014). Most Program Verification and Synthesis problems of interest can be modeled directly using Horn clauses and many recent advances in the Constraint/Logic Programming and Program Verification communities have centered around efficiently solving problems presented as Horn clauses. Since Horn clauses for verification and synthesis have been advocated by these communities in different times and from different perspectives, the HCVS workshop was organized to stimulate interaction and a fruitful exchange and integration of experiences.

cs.LO↗

arXiv2013

Verification of Imperative Programs by Constraint Logic Program Transformation

We present a method for verifying partial correctness properties of imperative programs that manipulate integers and arrays by using techniques based on the transformation of constraint logic programs (CLP). We use CLP as a metalanguage for representing imperative programs, their executions, and their properties. First, we encode the correctness of an imperative program, say prog, as the negation of a predicate 'incorrect' defined by a CLP program T. By construction, 'incorrect' holds in the least model of T if and only if the execution of prog from an initial configuration eventually halts in an error configuration. Then, we apply to program T a sequence of transformations that preserve its least model semantics. These transformations are based on well-known transformation rules, such as unfolding and folding, guided by suitable transformation strategies, such as specialization and generalization. The objective of the transformations is to derive a new CLP program TransfT where the predicate 'incorrect' is defined either by (i) the fact 'incorrect.' (and in this case prog is not correct), or by (ii) the empty set of clauses (and in this case prog is correct). In the case where we derive a CLP program such that neither (i) nor (ii) holds, we iterate the transformation. Since the problem is undecidable, this process may not terminate. We show through examples that our method can be applied in a rather systematic way, and is amenable to automation by transferring to the field of program verification many techniques developed in the field of program transformation.

cs.PL↗

arXiv2011

Generalization Strategies for the Verification of Infinite State Systems

We 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. To appear in Theory and Practice of Logic Programming (TPLP).

cs.LO↗

arXiv2004

Transformation Rules for Locally Stratified Constraint Logic Programs

We propose a set of transformation rules for constraint logic programs with negation. We assume that every program is locally stratified and, thus, it has a unique perfect model. We give sufficient conditions which ensure that the proposed set of transformation rules preserves the perfect model of the programs. Our rules extend in some respects the rules for logic programs and constraint logic programs already considered in the literature and, in particular, they include a rule for unfolding a clause with respect to a negative literal.

cs.PL↗