An Algorithm for Deciding BAPA: Boolean Algebra with Presburger Arithmetic

Abstract. Fault-tolerant distributed algorithms play an important role in ensuring the reliability of many software applications. In this paper we consider distributed algorithms whose computations are organized in rounds. To verify the correctness of such algorithms, we reason about (i) properties (such as invariants) of the state, (ii) the transitions controlled by the algorithm, and (iii) the communication graph. We introduce a logic that addresses these points, and contains set comprehensions with cardinality constraints, function symbols to describe the local states of each process, and a limited form of quantifier alternation to express the verification conditions. We show its use in automating the verification of consensus algorithms. In particular, we give a semi-decision procedure for the unsatisfiability problem of the logic and identify a decidable fragment.We successfully applied our framework to verify the correctness of a variety of consensus algorithms tolerant to both benign faults (message loss, process crashes) and value faults (message corruption).

Section: Related Workmentioning

confidence: 99%

A Logic-Based Framework for Verifying Consensus Algorithms

DrăźGoi

Henzinger

Veith

et al. 2014

“…Then, it is required that Λ(G 2 ) ⇒ Λ(G 1 ) [Γ]. Such a formula belongs for instance, to the fragment of BAPA [14], and thus its validity can be decided in NP-time. For the example in Fig.…”

Section: Noll Graph Homomorphismmentioning

confidence: 99%

Compositional Invariant Checking for Overlaid and Nested Linked Lists

Enea

Saveluc

Sighireanu

2013

Abstract. We introduce a fragment of separation logic, called NOLL, for automated reasoning about programs manipulating overlaid and nested linked lists, where overlaid means that the lists share the same set of objects. The distinguishing features of NOLL are: (1) it is parametrized by a set of user-defined predicates specifying nested linked list segments, (2) a "per-field" version of the separating conjunction allowing to share object locations but not record field locations, and (3) it can express sharing constraints between list segments. We prove that checking the entailment between two NOLL formulas is co-NP complete using a small model property. We also provide an effective procedure for checking entailment in NOLL, which first constructs a Boolean abstraction of the two formulas in order to infer all the implicit constraints, and then, it checks the existence of a homomorphism between the two formulas, viewed as graphs. We have implemented this procedure and applied it on verification conditions generated from several interesting case studies that manipulate overlaid and nested data structures.

“…Kuncak, et al give a decision procedure for a quantified language of sets of uninterpreted elements with cardinality constraints [14]. The language is known as BAPAboolean algebra with Presburger arithmetic.…”

Section: Related Workmentioning

confidence: 99%

Decision Procedures for Region Logic

Rosenberg

Banerjee

Naumann

2012

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.