Semirings, automata, languages
Semirings, automata, languages
Hierarchical correctness proofs for distributed algorithms
PODC '87 Proceedings of the sixth annual ACM Symposium on Principles of distributed computing
A methodology for solving Markov models of parallel systems
Journal of Parallel and Distributed Computing
Bisimulation through probabilistic testing
Information and Computation
Stochastic Automata Network of Modeling Parallel Systems
IEEE Transactions on Software Engineering
Reactive, generative, and stratified models of probabilistic processes
Information and Computation
A compositional approach to performance modelling
A compositional approach to performance modelling
Composition and behaviors of probabilistic I/O automata
Theoretical Computer Science
Information and Computation
Exact performance equivalence: an equivalence relation for stochastic automata
Theoretical Computer Science
Performance Evaluation of Computer and Communication Systems, Joint Tutorial Papers of Performance '93 and Sigmetrics '93
Composition and Behaviors of Probabilistic I/O Automata
CONCUR '94 Proceedings of the Concurrency Theory
Compositional Analysis of Expected Delays in Networks of Probabilistic I/O Automata
LICS '98 Proceedings of the 13th Annual IEEE Symposium on Logic in Computer Science
Weighted tree automata and weighted logics
Theoretical Computer Science
Bisimulation relations for weighted automata
Theoretical Computer Science
On the verification of probabilistic I/O automata with unspecified rates
Proceedings of the 2009 ACM symposium on Applied Computing
Weighted Bisimulation in Linear Algebraic Form
CONCUR 2009 Proceedings of the 20th International Conference on Concurrency Theory
A coalgebraic perspective on linear weighted automata
Information and Computation
Probabilistic i/o automata: theories of two equivalences
CONCUR'06 Proceedings of the 17th international conference on Concurrency Theory
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Previous work of the author has developed probabilistic input/output automata (PIOA) as a formalism for modelling systems that exhibit concurrent and probabilistic behaviour. Central to that work was the notion of the "behaviour map" associated with a state of a PIOA. The present paper presents a new, simpler definition for PIOA behaviour maps, investigates the induced "same behaviour map" equivalence relation, and compares it with the standard notion of probabilistic bisimulation equivalence. Weighted finite automata are used as a unifying formalism to facilitate the comparison. A general notion of congruence for weighted automata is defined, which relates signed measures on states, rather than just individual states. PIOA are defined as a class of weighted automata, as are the class of probabilistic weighted automata for which the standard definition of probabilistic bisimulation makes sense. A characterization is obtained of probabilistic bisimulation as the largest congruence that is in a sense generated by its restriction to a relation on states. This characterization is then used as the definition of weighted bisimulation, which generalizes probabilistic bisimulation to the full class of weighted automata. PIOA behaviour equivalence is also shown to define a weighted automata congruence, which is strictly refined by weighted bisimulation equivalence. The relationship between these congruences and a notion of composition for weighted automata is also examined.