Linear Ranking with Reachability

Bradley, Aaron R.; Manna, Zohar; Sipma, Henny B.

doi:10.1007/11513988_48

Cited by 178 publications

(222 citation statements)

References 19 publications

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“…The difference here is that we iteratively enrich the termination argument using successful calls to a constraint-based tool on slices of the program, whereas constraint-based ranking function synthesis tools (e.g. [4], [5], [21], etc) were originally applied to entire programs.…”

Section: Introductionmentioning

confidence: 99%

Ramsey vs. Lexicographic Termination Proving

Cook

See

Zuleger

2013

Tools and Algorithms for the Construction and Analysis of Systems

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Abstract. Termination proving has traditionally been based on the search for (possibly lexicographic) ranking functions. In recent years, however, the discovery of termination proof techniques based on Ramsey's theorem have led to new automation strategies, e.g. size-change, or iterative reductions from termination to safety. In this paper we revisit the decision to use Ramsey-based termination arguments in the iterative approach. We describe a new iterative termination proving procedure that instead searches for lexicographic termination arguments. Using experimental evidence we show that this new method leads to dramatic speedups.

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Section: Introductionmentioning

confidence: 99%

Ramsey vs. Lexicographic Termination Proving

Cook

See

Zuleger

2013

Tools and Algorithms for the Construction and Analysis of Systems

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“…Finding such ranking functions is not easy, and automation requires techniques adapted to specific data domains. Techniques have been developed for programs with integers or reals [12,13,14,18,19], functional programs, [25], and parameterized systems [22,23].…”

Section: Introductionmentioning

confidence: 99%

“…Automated construction of such ranking functions is a challenging task, which requires techniques adapted to specific data domains. Recently, significant progress has been achieved for programs that operate on numerical domains, integers or reals [12,13,14,18,19,21]. Rather few papers present efficient techniques to prove termination for programs that operate on arbitrary data domains.…”

Section: Introductionmentioning

confidence: 99%

Proving Liveness by Backwards Reachability

Abdulla

Jönsson

Rezine

et al. 2006

CONCUR 2006 – Concurrency Theory

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Abstract. We present a new method for proving liveness and termination properties for fair concurrent programs, which does not rely on finding a ranking function or on computing the transitive closure of the transition relation. The set of states from which termination or some liveness property is guaranteed is computed by a backwards reachability analysis. A central technique for handling concurrency is a check for certain commutativity properties. The method is not complete. However, it can be seen as a complement to other methods for proving termination, in that it transforms a termination problem into a simpler one with a larger set of terminated states. We show the usefulness of our method by applying it to existing programs from the literature. We have also implemented it in the framework of Regular Model Checking, and used it to automatically verify non-starvation for parameterized algorithms.

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“…Thus, an abstract state is given by a set of predicates a ⊆ Φ. 5 We sometimes represent a by a formula, namely the conjunction of predicates in a. For example, if a = {(x ≥ y), (0 ≤ x < n)} then we also represent a by the formula (x ≥ y) ∧ (0 ≤ x < n).…”

Section: Preliminariesmentioning

confidence: 99%

“…Recently, significant progress has been made by automatically proving termination [13,5,6,4]. The main idea is to synthesize ranking functions proving well foundedness.…”

Section: Introductionmentioning

confidence: 99%

Leaping Loops in the Presence of Abstraction

Ball

Kupferman

Sagiv

Computer Aided Verification

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Abstract. Finite abstraction helps program analysis cope with the huge state space of programs. We wish to use abstraction in the process of error detection. Such a detection involves reachability analysis of the program. Reachability in an abstraction that under-approximates the program implies reachability in the concrete system. Under-approximation techniques, however, lose precision in the presence of loops, and cannot detect their termination. This causes reachability analysis that is done with respect to an abstraction to miss states of the program that are reachable via loops. Current solutions to this loop-termination challenge are based on fair termination and involve the use of well-founded sets and ranking functions. In many cases, the concrete system has a huge, but still finite set of states. Our contribution is to show how, in such cases, it is possible to analyze termination of loops without refinement and without well-founded sets and ranking functions. Instead, our method is based on conditions on the structure of the graph that corresponds to the concrete system -conditions that can be checked with respect to the abstraction. We describe our method, demonstrate its usefulness and show how its application can be automated by means of a theorem prover.

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Linear Ranking with Reachability

Cited by 178 publications

References 19 publications

Ramsey vs. Lexicographic Termination Proving

Ramsey vs. Lexicographic Termination Proving

Proving Liveness by Backwards Reachability

Leaping Loops in the Presence of Abstraction

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