The quest for minimal quotients for probabilistic automata

Authors:
Christian Eisentraut;Holger Hermanns;Johann Schuster;Andrea Turrini;Lijun Zhang
Affiliations:
Department of Computer Science, Saarland University, Germany;Department of Computer Science, Saarland University, Germany;Department of Computer Science, University of the Federal Armed Forces Munich, Germany;Department of Computer Science, Saarland University, Germany;DTU Informatics, Technical University of Denmark, Denmark, Department of Computer Science, Saarland University, Germany
Venue:
TACAS'13 Proceedings of the 19th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Year:
2013

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Abstract

One of the prevailing ideas in applied concurrency theory and verification is the concept of automata minimization with respect to strong or weak bisimilarity. The minimal automata can be seen as canonical representations of the behaviour modulo the bisimilarity considered. Together with congruence results wrt. process algebraic operators, this can be exploited to alleviate the notorious state space explosion problem. In this paper, we aim at identifying minimal automata and canonical representations for concurrent probabilistic models. We present minimality and canonicity results for probabilistic automata wrt. strong and weak bisimilarity, together with polynomial time minimization algorithms.