449 research outputs found
Decidability of bisimulation equivalence for processes generating context-free languages
A context-free grammar (CFG) in Greibach Normal Form coincides, in another notation, with a system of guarded recursion equations in Basic Process Algebra. Hence to each CFG a process can be assigned as solution, which has as its set of finite traces the context-free language (CFL) determined by that CFG. While the equality problem for CFL's is unsolvable, the equality problem for the processes determined by CFG's turns out to be solvable. Here equality on processes is given by a model of process graphs modulo bisimulation equivalence. The proof is given by displaying a periodic structure of the process graphs determined by CFG's. As a corollary of the periodicity a short proof of the solvability of the equivalence problem for simple context-free languages is given
Decidability of bisimulation equivalence for processes generating context-free languages
A context-free grammar (CFG) in Greibach Normal Form coincides, in another notation, with a system of guarded recursion equations in Basic Process Algebra. Hence to each CFG a process can be assigned as solution, which has as its set of finite traces the context-free language (CFL) determined by that CFG. While the equality problem for CFL's is unsolvable, the equality problem for the processes determined by CFG's turns out to be solvable. Here equality on processes is given by a model of process graphs modulo bisimulation equivalence. The proof is given by displaying a periodic structure of the process graphs determined by CFG's. As a corollary of the periodicity a short proof of the solvability of the equivalence problem for simple context-free languages is given
A Polynomial Time Algorithm for Deciding Branching Bisimilarity on Totally Normed BPA
Strong bisimilarity on normed BPA is polynomial-time decidable, while weak
bisimilarity on totally normed BPA is NP-hard. It is natural to ask where the
computational complexity of branching bisimilarity on totally normed BPA lies.
This paper confirms that this problem is polynomial-time decidable. To our
knowledge, in the presence of silent transitions, this is the first
bisimilarity checking algorithm on infinite state systems which runs in
polynomial time. This result spots an instance in which branching bisimilarity
and weak bisimilarity are both decidable but lie in different complexity
classes (unless NP=P), which is not known before.
The algorithm takes the partition refinement approach and the final
implementation can be thought of as a generalization of the previous algorithm
of Czerwi\'{n}ski and Lasota. However, unexpectedly, the correctness of the
algorithm cannot be directly generalized from previous works, and the
correctness proof turns out to be subtle. The proof depends on the existence of
a carefully defined refinement operation fitted for our algorithm and the
proposal of elaborately developed techniques, which are quite different from
previous works.Comment: 32 page
Equivalence-Checking on Infinite-State Systems: Techniques and Results
The paper presents a selection of recently developed and/or used techniques
for equivalence-checking on infinite-state systems, and an up-to-date overview
of existing results (as of September 2004)
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