Abstract
We study the parallel complexity of three problems on concurrency: decision of firing sequences for Petri nets, trace equivalence for partially commutative monoids, and strong bisimilarity in finite transition systems. We show that the first two problems can be efficiently parallelized, allowing logarithmic time Parallel RAM algorithms and even constant time unbounded fan-in circuits with threshold gates. However, lower bounds imply that they cannot be solved in constant time by a PRAM algorithm. On the other hand, strong bisimilarity in finite labelled transition systems can be classified as P-complete; as a consequence, algorithms for automated analysis of finite state systems based on bisimulation seem to be inherently sequential in the following sense: the design of an efficient parallel algorithm to solve any of these problems will require an exceedingly hard algorithmic breakthrough.
Research supported by the ESPRIT II Basic Research Actions Program of the EC under contract No. 3075 (project ALCOM).
Research supported by the Programme MERCURE of the DCSTD of the Ministère Français des Affaires Etrangères and the DGICYT of the Ministerio de Educación y Ciencia de Espaňa. This research was performed while visiting the Dep. de Llenguatges i Sistemes Informàtics of the Universitat Politècnica de Catalunya.
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Àlvarez, C., Balcázar, J.L., Gabarró, J., Sántha, M. (1991). Parallel complexity in the design and analysis of concurrent systems. In: Aarts, E.H.L., van Leeuwen, J., Rem, M. (eds) Parle ’91 Parallel Architectures and Languages Europe. Lecture Notes in Computer Science, vol 505. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-25209-3_20
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