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Alltermination(T
 In Proceedings of TACAS2009, volume 5505 of LNCS
, 2009
"... Abstract We introduce the AllTermination(T ) problem: given a termination solver, T , and a program (a set of functions), find every set of formal arguments whose consideration is sufficient to show the program terminating using T . One important and motivating application is enhancing theorem pro ..."
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Abstract We introduce the AllTermination(T ) problem: given a termination solver, T , and a program (a set of functions), find every set of formal arguments whose consideration is sufficient to show the program terminating using T . One important and motivating application is enhancing theorem proving systems by constructing the set of strongest induction schemes for a program, modulo T . These schemes can be derived from the set of termination cores, the minimal sets returned by AllTermination(T ). We study the AllTermination(T ) problem as applied to two existing termination analyses: general sizechange (SCT ) and polynomial sizechange (SCP ). We analyze the intrinsic complexity of the problems and develop algorithms that we expect to perform well in practice. We show that AllTermination(SCT ) is a PSpacecomplete problem. We also show that no outputpolynomial algorithm exists for AllTermination(SCP ) (unless P = NP). Finally, we develop practical algorithms, some based on SATsolving, for both problems.
A New Algorithm for the Transversal Hypergraph Problem
, 1999
"... The Transversal Hypergraph Problem is the problem of generating, given a hypergraph, the set of its transversals, i.e. the hypergraph whose hyperedges are all minimal hitting sets of the given one. This problem turns out to be central in various fields of Computer Science. ..."
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The Transversal Hypergraph Problem is the problem of generating, given a hypergraph, the set of its transversals, i.e. the hypergraph whose hyperedges are all minimal hitting sets of the given one. This problem turns out to be central in various fields of Computer Science.