The size-change principle for program termination

Lee, Chin Soon; Jones, Neil D.; Ben-Amram, Amir M.

doi:10.1145/360204.360210

Cited by 237 publications

(257 citation statements)

References 10 publications

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“…Recent tools (e.g. [3], [8], [14], [15], etc) have moved away from single ranking functions and towards termination arguments based on Ramsey's theorem (e.g. [7], [9], [11], [22], etc).…”

Section: Introductionmentioning

confidence: 99%

“…Thus, the proof of a termination argument's validity is much harder. In size-change [15] or variance analysis [3] the result is imprecision: the tools are fast but can only prove a limited set of programs due to inaccuracies in the underlying abstractions that facilitate reasoning about the transitive closure. In iterative-based approaches (e.g.…”

Section: Introductionmentioning

confidence: 99%

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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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“…Recent tools (e.g. [3], [8], [14], [15], etc) have moved away from single ranking functions and towards termination arguments based on Ramsey's theorem (e.g. [7], [9], [11], [22], etc).…”

Section: Introductionmentioning

confidence: 99%

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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“…Lee et al [2001] proved that termination of a multiple-path ILC loop, when the constraints are restricted to size-change constraints (i.e., constraints of the form X i > X j or X i ≥ X j over N), is PSPACE-complete. Ben-Amram and Lee [2007] and Ben-Amram and Codish [2008] identified sub-classes of such loops for which the termination can be decided in, respectively, PTIME and NPTIME.…”

Section: Related Workmentioning

confidence: 99%

“…Very often, the state of the program during the loop is represented by a finite set of scalar variables (this simplification may be the result of an abstraction, such as size abstraction of structured data Lee et al 2001;Bruynooghe et al 2007;Spoto et al 2010]). …”

Section: Introductionmentioning

confidence: 99%

On the Termination of Integer Loops

Ben-Amram

Genaim

Masud

2012

Lecture Notes in Computer Science

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In this paper we study the decidability of termination of several variants of simple integer loops, without branching in the loop body and with affine constraints as the loop guard (and possibly a precondition). We show that termination of such loops is undecidable in some cases, in particular, when the body of the loop is expressed by a set of linear inequalities where the coefficients are from Z∪{r} with r an arbitrary irrational; when the loop is a sequence of instructions, that compute either linear expressions or the step function; and when the loop body is a piecewise linear deterministic update with two pieces. The undecidability result is proven by a reduction from counter programs, whose termination is known to be undecidable. For the common case of integer linear-constraint loops with rational coefficients we have not succeeded in proving either decidability or undecidability of termination, but we show that a Petri net can be simulated with such a loop; this implies some interesting lower bounds. For example, termination for a partially-specified input is at least EXPSPACE-hard.

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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%

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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The size-change principle for program termination

Cited by 237 publications

References 10 publications

Ramsey vs. Lexicographic Termination Proving

Ramsey vs. Lexicographic Termination Proving

On the Termination of Integer Loops

Proving Liveness by Backwards Reachability

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