Handling Parameterized Systems with Non-atomic Global Conditions

Lecture Notes in Computer Science

Cederberg

Vojnar

2011

Self Cite

Abstract. We investigate the use of monotonic abstraction and backward reachability analysis as means of performing shape analysis on programs with multiply pointed structures. By encoding the heap as a vertex-and edge-labeled graph, we can model the low level behaviour exhibited by programs written in the C programming language. Using the notion of signatures, which are predicates that define sets of heaps, we can check properties such as absence of null pointer dereference and shape invariants. We report on the results from running a prototype based on the method on several programs such as insertion into and merging of doubly-linked lists.

Section: Heapsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Monotonic Abstraction for Programs with Multiply-Linked Structures

Lecture Notes in Computer Science

Cederberg

Vojnar

2011

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“…Hence, proving a safety property in the abstract system implies that the property also holds in the original system. For a more technical description of the method and its application to non-trivial examples see, e.g., [4,3,13,5].…”

Section: Introductionmentioning

confidence: 99%

Forcing Monotonicity in Parameterized Verification: From Multisets to Words

SOFSEM 2010: Theory and Practice of Computer Science

2010

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Abstract. We present a tutorial on verification of safety properties for parameterized systems. Such a system consists of an arbitrary number of processes; the aim is to prove correctness of the system regardless of the number of processes inside the system. First, we consider a class of parameterized systems whose behaviours can be captured exactly as Petri nets using counter abstraction. This allows analysis using the framework of monotonic transition systems introduced in [1]. Then, we consider parameterized systems for which there is no natural ordering which allows monotonicity. We describe the method of monotonic abstraction which provides an over-approximation of the transition system. We consider both systems where the over-approximation gives rise to reset Petri nets, and systems where the abstract transition relation is a set of rewriting rules on words over a finite alphabet.

“…In [3,5,2] we have applied monotonic abstraction to other types of parameterized systems. More precisely, in [3] we have considered parameterized systems in which individual processes have local variables ranging over natural numbers; in [5] we have considered parameterized systems in which global conditions are evaluated non-atomically, finally, in [2] we have considered parameterized systems in which processes have a tree-like structure. Although defined on a common concept (monotonic abstraction of the transition system), the method presented in this paper is defined on a different class of parameterized systems than those studied in [3,5,2].…”

Section: Introductionmentioning

confidence: 99%

Monotonic Abstraction: On Efficient Verification of Parameterized Systems

Int. J. Found. Comput. Sci.

Delzanno

Henda

et al. 2009

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We introduce the simple and efficient method of monotonic abstraction to prove safety properties for parameterized systems with linear topologies. A process in the system is a finite-state automaton, where the transitions are guarded by both local and global conditions. Processes may communicate via broadcast, rendez-vous and shared variables over finite domains. The method of monotonic abstraction derives an over-approximation of the induced transition system that allows the use of a simple class of regular expressions as a symbolic representation. Compared to traditional regular model checking methods, the analysis does not require the manipulation of transducers, and hence its simplicity and efficiency. We have implemented a prototype that works well on several mutual exclusion algorithms and cache coherence protocols.