Monte-Carlo approximation algorithms for enumeration problems
Journal of Algorithms
Randomized algorithms
Stubborn set methods for process algebras
POMIV '96 Proceedings of the DIMACS workshop on Partial order methods in verification
Stable models for stubborn sets
Fundamenta Informaticae - Special issue on Concurrency specification and programming (CS&P)
Minimizing the number of successor states in the stubborn set method
Fundamenta Informaticae
A Short Guide To Approximation Preserving Reductions
CCC '97 Proceedings of the 12th Annual IEEE Conference on Computational Complexity
Constraint Satisfaction: The Approximability of Minimization Problems
CCC '97 Proceedings of the 12th Annual IEEE Conference on Computational Complexity
On some central problems in computational complexity.
On some central problems in computational complexity.
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This article continues research on the stubborn set method that constructs on-the-fly a reduced LTS that is CFFD-equivalent to the parallel composition of given LTSs. In particular, minimization of the number of successor states of a given state is reconsidered. The earlier suggested and/or-graph approach requires solving #P-complete counting problems in order to get the weights for the vertices of the and/or-graph. The "branch-and-bound" decision problem corresponding to the minimization of the sum of the computed weights is "only" NP-complete. Unfortunately, #P-complete counting does not seem easily avoidable in the general case because it is PP-complete to check whether a given stubborn set produces at most as many successor states as another given stubborn set. Instead of solving each of the subproblems, one could think of computing approximate solutions in such a way that the total effect of the approximations is a useful approximation itself.