[Paper Review] Late Weak Bisimulation for Markov Automata

Eisentraut, Christian, Jens Chr. Godskesen+3 more|arXiv (Cornell University)|Feb 18, 2012

Formal Methods in Verification11 references20 citations

TL;DR

This paper introduces late weak bisimilarity for Markov automata, a coarser equivalence relation than standard weak bisimilarity that preserves trace distribution equivalence under partial information schedulers and compositionality under distributed schedulers. By restricting to the intersection of these scheduler classes, the relation achieves a coarser yet still reasonable and compositional behavioral equivalence for stochastic systems with both probabilistic and nondeterministic choices.

ABSTRACT

Weak bisimilarity is a distribution-based equivalence notion for Markov automata. It has gained some popularity as the coarsest reasonable behavioural equivalence on Markov automata. This paper studies a strictly coarser notion: Late weak bisimilarity enjoys valuable properties if restricting to important subclasses of schedulers: Trace distribution equivalence is implied for partial information schedulers, and compositionality is preserved by distributed schedulers. The intersection of the two scheduler classes thus spans a coarser and still reasonable compositional theory of Markov automata.

Motivation & Objective

• To address the limitation of standard weak bisimilarity in distinguishing systems that are intuitively equivalent under realistic observer models.
• To define a coarser behavioral equivalence that maintains desirable properties like trace distribution equivalence and compositionality.
• To identify a restricted class of schedulers where late weak bisimilarity is both compositional and implies trace distribution equivalence.
• To provide a foundation for compositional verification of Markov automata under practical scheduling assumptions.

Proposed method

• Proposes late weak bisimilarity as a new equivalence relation on subprobability distributions, extending weak bisimilarity for Markov automata.
• Introduces two key scheduler classes: partial information schedulers (where decisions depend only on observable actions) and distributed schedulers (where decisions are made locally without global knowledge).
• Analyzes the behavior of systems under the intersection of these scheduler classes to ensure both trace distribution equivalence and compositionality.
• Uses a CSP-style parallel composition with synchronization to model system interactions and evaluate behavioral equivalence.
• Employs a counterexample-based analysis to show that standard weak bisimilarity fails to equate intuitively equivalent systems under certain unrealistic schedulers.
• Establishes that late weak bisimilarity coincides with the coarsest congruence preserving trace distribution equivalence when restricted to the intersection of partial information and distributed schedulers.

Experimental results

Research questions

• RQ1 Can a coarser behavioral equivalence be defined for Markov automata that still preserves trace distribution equivalence under partial information schedulers?
• RQ2 Does late weak bisimilarity maintain compositionality when restricted to distributed schedulers?
• RQ3 Is there a common subclass of schedulers where late weak bisimilarity is both trace-preserving and compositional?
• RQ4 How does late weak bisimilarity compare to standard weak bisimilarity in terms of discriminating systems that are intuitively equivalent?
• RQ5 Can late weak bisimilarity be characterized as the coarsest congruence preserving trace distribution equivalence under realistic scheduling assumptions?

Key findings

• Late weak bisimilarity is strictly coarser than standard weak bisimilarity and resolves counterintuitive distinctions in systems like the coin-tossing example.
• Under partial information schedulers, late weak bisimilarity implies trace distribution equivalence, ensuring equivalent observable behavior.
• Under distributed schedulers, late weak bisimilarity preserves compositionality, enabling modular verification.
• The intersection of partial information and distributed schedulers ensures that late weak bisimilarity is both trace-preserving and compositional.
• Late weak bisimilarity is the coarsest congruence preserving trace distribution equivalence when restricted to the intersection of the two scheduler classes.
• The decision procedure for late weak bisimilarity is expected to be simpler than for standard weak bisimilarity, as it avoids arbitrary splitting of distributions.