Applying Reversibility Theory for the Performance Evaluation of Reversible Computations

Balsamo, Simonetta; Cavallin, Filippo; Marin, Andrea; Rossi, Sabina

doi:10.1007/978-3-319-43904-4_4

Cited by 1 publication

(1 citation statement)

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“…In [9] the authors propose the idea of using a general permutation of states for comparing forward and reversed processes at continuous time. A review covering the main results regarding time-reversible Markov processes and a discussion about how to apply them to tackle the problem of the quantitative evaluation of reversible computations can be found in [1]. In [4] the authors show new results on both reversed stationary Markov processes as well as Markovian process algebra.…”

Section: Introductionmentioning

confidence: 99%

Efficient Computation of Renaming Functions for ρ-reversible Discrete and Continuous Time Markov Chains

Sottana

Piazza

Albarelli

2017

Proceedings of the 11th EAI International Conference on Performance Evaluation Methodologies and Tools

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With the introduction of ρ-reversibility, the basic notion of reversible Markov chain has been relaxed by allowing a wider range of scenarios. Specifically, the reversibility properties are not just sought on the chain itself, but also on all the possible topology-preserving renamings of its state space. Such renamings, called Renaming Functions, exhibit many interesting properties which can be exploited in different contexts. Unfortunately, finding a renaming function for a Markov chain is a very computationally intensive task. Using a naive approach it could require to check for all the possible state space permutations, which is unfeasible for all but the most trivial chains. As a matter of fact, we prove that the corresponding decision problem is polynomially equivalent to Graph Isomorphism. Nevertheless, we introduce an algorithm that, exploiting some necessary conditions for ρ-reversibility, is able to efficiently prune the search space and then verify the remaining renaming candidates. The correctness of the method is theoretically demonstrated and its practical effectiveness is shown over a significant set of discrete and continuous ρ-reversible Markov chains.

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Section: Introductionmentioning

confidence: 99%