Collections, Cardinalities, and Relations

Yessenov, Kuat; Piskač, Ružica; Kunčak, Viktor

doi:10.1007/978-3-642-11319-2_27

Cited by 28 publications

(26 citation statements)

References 27 publications

(60 reference statements)

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“…2 to require alloc to be interpreted as a finite set. (The proof builds on ideas of [10,26].) By imposing simple syntactic restrictions we obtain a theory for which satisfiability is NP-complete, yet which is expressive enough to encompass the verification conditions that arise from the specifications we have used in case studies [1,22].…”

Section: Restricted-rl E -Tableau Calculusmentioning

confidence: 99%

“…Yessenov, et al introduce a decidable language QFBAPA-Rel with image expressions under unary function symbols and predicate symbols of any arity [26]. As in QFBAPA, the element sort is un-interpreted.…”

Section: Related Workmentioning

confidence: 99%

“…For a function f : A → A and set X ⊆ A, the decision procedure of [26] eliminates terms of the form f [X ] by first rewriting X as a union of (disjoint) Venn regions, i.e.,…”

Section: Related Workmentioning

confidence: 99%

“…There has been great progress in automated reasoning about sets and related theories, notably [26,24], but as we discuss in Sect. 6 prior work does not fully reach our goal.…”

Section: Introductionmentioning

confidence: 99%

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Decision Procedures for Region Logic

Rosenberg

Banerjee

Naumann

2012

Lecture Notes in Computer Science

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Abstract. Region logic is Hoare logic for object-based programs. It features local reasoning with frame conditions expressed in terms of sets of heap locations. This paper studies tableau-based decision procedures for RL, the quantifier-free fragment of the assertion language. This fragment combines sets and (functional) images with the theories of arrays and partial orders. The procedures are of practical interest because they can be integrated efficiently into the satisfiability modulo theories (SMT) framework. We provide a semi-decision procedure for RL and its implementation as a theory plugin inside the SMT solver Z3. We also provide a decision procedure for an expressive fragment of RL termed restricted-RL. We prove that deciding satisfiability of restricted-RL formulas is NP-complete. Both procedures are proven sound and complete. Preliminary performance results indicate that the semi-decision procedure has the potential toscale to large input formulas.

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Section: Restricted-rl E -Tableau Calculusmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

“…For a function f : A → A and set X ⊆ A, the decision procedure of [26] eliminates terms of the form f [X ] by first rewriting X as a union of (disjoint) Venn regions, i.e.,…”

Section: Related Workmentioning

confidence: 99%

“…There has been great progress in automated reasoning about sets and related theories, notably [26,24], but as we discuss in Sect. 6 prior work does not fully reach our goal.…”

Section: Introductionmentioning

confidence: 99%

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Decision Procedures for Region Logic

Rosenberg

Banerjee

Naumann

2012

Lecture Notes in Computer Science

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“…We discuss several examples in the paper. Moreover, the reduction to BAPA makes it possible to combine this logic with a number of other BAPA-reducible logics [17,21,23,24]. Therefore, we believe that our logic will be a useful component of verification tools in the near future.…”

Section: Introductionmentioning

confidence: 99%

Deciding Functional Lists with Sublist Sets

Wies

Muñiz

Kunčak

2012

Verified Software: Theories, Tools, Experiments

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Abstract.Motivated by the problem of deciding verification conditions for the verification of functional programs, we present new decision procedures for automated reasoning about functional lists. We first show how to decide in NP the satisfiability problem for logical constraints containing equality, constructor, selectors, as well as the transitive sublist relation. We then extend this class of constraints with operators to compute the set of all sublists, and the set of objects stored in a list. Finally, we support constraints on sizes of sets, which gives us the ability to compute list length as well as the number of distinct list elements. We show that the extended theory is reducible to the theory of sets with linear cardinality constraints, and therefore still in NP. This reduction enables us to combine our theory with other decidable theories that impose constraints on sets of objects, which further increases the potential of our decidability result in verification of functional and imperative software.

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Counting Constraints in Flat Array Fragments

Alberti¹,

Ghilardi

Pagani

2016

Automated Reasoning

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We identify a fragment of Presburger arithmetic enriched with free function symbols and cardinality constraints for interpreted sets, which is amenable to automated analysis. We establish decidability and complexity results for such a fragment and we implement our algorithms. The experiments run in discharging proof obligations coming from invariant checking and bounded model-checking benchmarks show the practical feasibility of our decision procedure.

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Collections, Cardinalities, and Relations

Cited by 28 publications

References 27 publications

Decision Procedures for Region Logic

Decision Procedures for Region Logic

Deciding Functional Lists with Sublist Sets

Counting Constraints in Flat Array Fragments

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