DeepAI AI Chat
Log In Sign Up

Explaining Behavioural Inequivalence Generically in Quasilinear Time

by   Thorsten Wißmann, et al.

We provide a generic algorithm for constructing formulae that distinguish behaviourally inequivalent states in systems of various transition types such as nondeterministic, probabilistic or weighted; genericity over the transition type is achieved by working with coalgebras for a set functor in the paradigm of universal coalgebra. For every behavioural equivalence class, we construct a formula which holds precisely at the states in that class. The algorithm instantiates to deterministic finite automata, transition systems, labelled Markov chains, and systems of many other types. The ambient logic is a modal logic featuring modalities that are generically derived from the functor. The new algorithm builds on an existing coalgebraic partition refinement algorithm. It runs in time O((m + n) log n) on systems with n states and m transitions, and the same asymptotic bound applies to the dag size of the formulae it constructs. This improves the bounds on run time and formula size compared to previous algorithms even for previously known specific instances, viz. transition systems and Markov chains; in particular, the best previous bound for transition systems was O(mn).


page 1

page 2

page 3

page 4


Quasilinear-time Computation of Generic Modal Witnesses for Behavioural Inequivalence

We provide a generic algorithm for constructing formulae that distinguis...

A simpler O(m log n) algorithm for branching bisimilarity on labelled transition systems

Branching bisimilarity is a behavioural equivalence relation on labelled...

Lowerbounds for Bisimulation by Partition Refinement

We provide time lower bounds for sequential and parallel algorithms deci...

Rate Reduction for State-labelled Markov Chains with Upper Time-bounded CSL Requirements

This paper presents algorithms for identifying and reducing a dedicated ...

From Generic Partition Refinement to Weighted Tree Automata Minimization

Partition refinement is a method for minimizing automata and transition ...

Distributed Coalgebraic Partition Refinement

Partition refinement is a method for minimizing automata and transition ...

Building Squares with Optimal State Complexity in Restricted Active Self-Assembly

Tile Automata is a recently defined model of self-assembly that borrows ...