A fast algorithm for deciding bisimilarity of normed context-free processes

Abstract

Until recently, algorithms for deciding bisimulation equivalence between normed context-free processes have all been nondeterministic. The optimal such algorithm, due to Huynh and Tian, is in Σ ^P₂ =NP^NP: it guesses a proof of equivalence and validates this proof in polynomial time using oracles freely answering questions which are in NP. Hirshfeld, Jerrum and Moller have since demonstrated that this problem is actually decidable in polynomial time. However, this algorithm is far from being practical, giving a O(n ¹³) algorithm, where n is (roughly) the size of the grammar defining the processes, that is, the number of symbols in its description. In this paper we present a deterministic algorithm which runs in time O(n ⁴ v) where v is the norm of the processes being compared, which corresponds to the shortest distance to a terminating state of the process, or the shortest word generated by the corresponding grammar. Though this may be exponential, it still appears to be efficient in practice, when norms are typically of moderate size. Also, the algorithm tends to behave well even when the norm is exponentially large. Furthermore, we believe that the techniques may lead to more efficient polynomial algorithms; indeed we have not been able to find an example for which our optimised algorithm requires exponential time.

The first author is on Sabbatical leave from The School of Mathematics and Computer Science, Tel Aviv University.

The second author is supported by Esprit Basic Basic Research Action No.7166 “CON-CUR2” and is currently at the Swedish Institute of Computer Science.