Monotonic Abstraction for Programs With Multiply-Linked Structures

Abdulla, Parosh Aziz; Cederberg, Jonathan; Vojnar, Tomáš

doi:10.1142/s0129054113400078

Cited by 4 publications

(2 citation statements)

References 8 publications

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“…In [6,7], monotonic abstractions are defined for linked data structures. The wqo on heaps defined there is semantically similar to ∀ * with n * , but it is defined via tree operations and not via logic.…”

Section: Related Workmentioning

confidence: 99%

Decidability of inferring inductive invariants

Padon

Immerman

Shoham

et al. 2016

Proceedings of the 43rd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

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Induction is a successful approach for verification of hardware and software systems. A common practice is to model a system using logical formulas, and then use a decision procedure to verify that some logical formula is an inductive safety invariant for the system. A key ingredient in this approach is coming up with the inductive invariant, which is known as invariant inference. This is a major difficulty, and it is often left for humans or addressed by sound but incomplete abstract interpretation. This paper is motivated by the problem of inductive invariants in shape analysis and in distributed protocols. This paper approaches the general problem of inferring firstorder inductive invariants by restricting the language L of candidate invariants. Notice that the problem of invariant inference in a restricted language L differs from the safety problem, since a system may be safe and still not have any inductive invariant in L that proves safety. Clearly, if L is finite (and if testing an inductive invariant is decidable), then inferring invariants in L is decidable. This paper presents some interesting cases when inferring inductive invariants in L is decidable even when L is an infinite language of universal formulas. Decidability is obtained by restricting L and defining a suitable well-quasi-order on the state space. We also present some undecidability results that show that our restrictions are necessary. We further present a framework for systematically constructing infinite languages while keeping the invariant inference problem decidable. We illustrate our approach by showing the decidability of inferring invariants for programs manipulating linked-lists, and for distributed protocols.

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Section: Related Workmentioning

confidence: 99%

Decidability of inferring inductive invariants

Padon

Immerman

Shoham

et al. 2016

Proceedings of the 43rd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

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show abstract

“…Coverability for automata-based models of broadcast communication has recently been studied in [15,16,13,18,12]. In the context of program analysis approximated backward search working on graphs representing data structures with pointers have been considered in [2]. In this setting approximations are defined via edges or node deletion.…”

Section: Conclusion and Related Workmentioning

confidence: 99%

Parameterized Verification of Graph Transformation Systems with Whole Neighbourhood Operations

Delzanno

Stückrath

2014

Lecture Notes in Computer Science

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We introduce a new class of graph transformation systems in which rewrite rules can be guarded by universally quantified conditions on the neighbourhood of nodes. These conditions are defined via special graph patterns which may be transformed by the rule as well. For the new class for graph rewrite rules, we provide a symbolic procedure working on minimal representations of upward closed sets of configurations. We prove correctness and effectiveness of the procedure by a categorical presentation of rewrite rules as well as the involved order, and using results for well-structured transition systems. We apply the resulting procedure to the analysis of the Distributed Dining Philosophers protocol on an arbitrary network structure.

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Parameterized verification

Abdulla

Delzanno

2016

Int J Softw Tools Technol Transfer

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The goal of parameterized verification is to prove the correctness of a system specification regardless of the number of its components. The problem is of interest in several different areas: verification of hardware design, multithreaded programs, distributed systems, and communication protocols. The problem is undecidable in general. Solutions for restricted classes of systems and properties have been studied in areas like theorem proving, model checking, automata and logic, process algebra, and constraint solving. In this introduction to the special issue, dedicated to a selection of works from the Parameterized Verification workshop PV ’14 and PV ’15, we survey some of the works developed in this research area

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Monotonic Abstraction for Programs With Multiply-Linked Structures

Cited by 4 publications

References 8 publications

Decidability of inferring inductive invariants

Decidability of inferring inductive invariants

Parameterized Verification of Graph Transformation Systems with Whole Neighbourhood Operations

Parameterized verification

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