Synchronizing Constrained Horn Clauses

Mordvinov, Dmitry; Fedyukovich, Grigory

doi:10.29007/gr5c

Cited by 17 publications

(32 citation statements)

References 16 publications

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“…The first one consists in the incorporation into the CHC solvers of appropriate induction principles [22,25]. The second one consists in transforming the given set of CHCs into a new set where inductively defined data structures are removed, and whose satisfiability implies the satisfiability of the original clauses [10,19].…”

Section: Introductionmentioning

confidence: 99%

Lemma Generation for Horn Clause Satisfiability: A Preliminary Study

Angelis

Fioravanti

Pettorossi

et al. 2019

Electron. Proc. Theor. Comput. Sci.

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It is known that the verification of imperative, functional, and logic programs can be reduced to the satisfiability of constrained Horn clauses (CHCs), and this satisfiability check can be performed by using CHC solvers, such as Eldarica and Z3. These solvers perform well when they act on simple constraint theories, such as Linear Integer Arithmetic and the theory of Booleans, but their efficacy is very much reduced when the clauses refer to constraints on inductively defined structures, such as lists or trees. Recently, we have presented a transformation technique for eliminating those inductively defined data structures, and hence avoiding the need for incorporating induction principles into CHC solvers. However, this technique may fail when the transformation requires the use of lemmata whose generation needs ingenuity. In this paper we show, through an example, how during the process of transforming CHCs for eliminating inductively defined structures one can introduce suitable predicates, called difference predicates, whose definitions correspond to the lemmata to be introduced. Through a second example, we show that, whenever difference predicates cannot be introduced, we can introduce, instead, auxiliary queries which also correspond to lemmata, and the proof of these lemmata can be done by showing the satisfiability of those queries.

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Section: Introductionmentioning

confidence: 99%

Lemma Generation for Horn Clause Satisfiability: A Preliminary Study

Angelis

Fioravanti

Pettorossi

et al. 2019

Electron. Proc. Theor. Comput. Sci.

View full text Add to dashboard Cite

show abstract

“…In order to overcome this difficulty, the following two approaches have recently been suggested. (i) The first one consists in the incorporation into CHC solvers of suitable induction principles [20,22], and (ii) the second one consists in transforming the given set of CHCs into a new set where inductively defined data structures are removed, and whose satisfiability implies the satisfiability of the original clauses [8,18].…”

Section: Introductionmentioning

confidence: 99%

Proving Properties of Sorting Programs: A Case Study in Horn Clause Verification

Angelis

Fioravanti

Pettorossi

et al. 2019

Electron. Proc. Theor. Comput. Sci.

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The proof of a program property can be reduced to the proof of satisfiability of a set of constrained Horn clauses (CHCs) which can be automatically generated from the program and the property. In this paper we have conducted a case study in Horn clause verification by considering several sorting programs with the aim of exploring the effectiveness of a transformation technique which allows us to eliminate inductive data structures such as lists or trees. If this technique is successful, we derive a set of CHCs with constraints over the integers and booleans only, and the satisfiability check can often be performed in an effective way by using state-of-the-art CHC solvers, such as Eldarica or Z3. In this case study we have also illustrated the usefulness of a companion technique based on the introduction of the so-called difference predicates, whose definitions correspond to lemmata required during the verification. We have considered functional programs which implement the following kinds of sorting algorithms acting on lists of integers: (i) linearly recursive sorting algorithms, such as insertion sort and selection sort, and (ii) non-linearly recursive sorting algorithms, such as quicksort and mergesort, and we have considered the following properties: (i) the partial correctness properties, that is, the orderedness of the output lists, and the equality of the input and output lists when viewed as multisets, and (ii) some arithmetic properties, such as the equality of the sum of the elements before and after sorting.Recent work has shown that constrained Horn clauses (CHCs) provide a suitable basis for program verification [1], and indeed many program verification problems can be reduced in a very natural way to CHC satisfiability problems. This fact has motivated the development of a number of tools, called CHC solvers, which can perform satisfiability proofs. Most of them work well on CHCs with simple constraint theories, such as the theory of Linear Integer Arithmetic (LIA) and the theory of Booleans (Bool). Among these tools we mention: Eldarica [14], FreqHorn [11], HSF [12], RAHFT [15], Spacer [16], VeriMAP [4], and Z3 [19].Unfortunately, when the properties to be verified refer to programs that act on inductively defined data structures, such as lists or trees, then the satisfiability proofs via CHC solvers becomes much harder, or even impossible, because those solvers do not natively incorporate induction principles relative to those data structures.

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“…Other instantiations, e.g., on top of a Horn solver based on Property-Directed Reachability [24] are possible, but outside the scope of this work. Synchronization.…”

Section: Instantiation Of Strategies In Forward Analysismentioning

confidence: 99%

“…Other automatic efforts for relational verification typically use some kind of product programs [6,13,17,21,22,24,28], with a possible reduction to Horn solving [13,17,21,24]. Similarly to our strategy for synchrony, most of them attempt to leverage similarity (structural or functional) in programs to ease verification.…”

Section: Related Workmentioning

confidence: 99%

“…In contrast, a parallel composition would provide potential for aligning the loop bodies, where relational invariants may be easier to establish than a functional loop invariant. Examples of techniques that exploit opportunities for such alignment include use of type-based analysis with self-composition [29], allowing flexibility in composition to be a mix of sequential and parallel [6], exploiting structurally equivalent programs for compiler validation [32], lockstep execution of loops in reasoning using Cartesian Hoare Logic [27], and merging Horn clause rules for relational verification [13,24].…”

Section: Introductionmentioning

confidence: 99%

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Exploiting Synchrony and Symmetry in Relational Verification

Pick

Fedyukovich

Gupta

2018

Computer Aided Verification

Self Cite

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Abstract. Relational safety specifications describe multiple runs of the same program or relate the behaviors of multiple programs. Approaches to automatic relational verification often compose the programs and analyze the result for safety, but a naively composed program can lead to difficult verification problems. We propose to exploit relational specifications for simplifying the generated verification subtasks. First, we maximize opportunities for synchronizing code fragments. Second, we compute symmetries in the specifications to reveal and avoid redundant subtasks. We have implemented these enhancements in a prototype for verifying k-safety properties on Java programs. Our evaluation confirms that our approach leads to a consistent performance speedup on a range of benchmarks.

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Synchronizing Constrained Horn Clauses

Cited by 17 publications

References 16 publications

Lemma Generation for Horn Clause Satisfiability: A Preliminary Study

Lemma Generation for Horn Clause Satisfiability: A Preliminary Study

Proving Properties of Sorting Programs: A Case Study in Horn Clause Verification

Exploiting Synchrony and Symmetry in Relational Verification

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