Abstract
We present a minimization algorithm for non-deterministic finite state automata that finds and merges bisimulation-equivalent states. The bisimulation relation is computed through partition aggregation, in contrast to existing algorithms that use partition refinement. The algorithm simultaneously generalises and simplifies an earlier one by Watson and Daciuk for deterministic devices. We show the algorithm to be correct and run in time O left( n^2 r^2 left| varSigma right| right) , where n is the number of states of the input automaton M, r is the maximal out-degree in the transition graph for any combination of state and input symbol, and left| varSigma right| is the size of the input alphabet. The algorithm has a higher time complexity than derivatives of Hopcroft’s partition-refinement algorithm, but represents a promising new solution approach that preserves language equivalence throughout the computation process. Furthermore, since the algorithm essentially computes the maximal model of a logical formula derived from M, optimisation techniques from the field of model checking become applicable.
Highlights
Finite-state automata is a fundamental concept in theoretical computer science, and their computational and representational complexity is the subject of extensive investigations
In the case of deterministic finite state automata, it is well-known that M is always unique and canonical with respect to the recognized language
Our work is to the best of our knowledge the first in which the bisimulation relation is computed through partition aggregation
Summary
Finite-state automata (nfa) is a fundamental concept in theoretical computer science, and their computational and representational complexity is the subject of extensive investigations. The currently predominant method of finding E is through partition refinement: The states are initially divided into final and non-final states, and the minimization algorithm resolves contradictions to the bisimulation condition by refining the partition until a fixed point is reached This method is fast, and requires O(m log n) computation steps (see [20]), where m is the size of M’s transition function. Our algorithm runs in O n2 |Σ| , which is the same as for the fastest aggregation-based dfa minimisation algorithms Another contribution is the computational approach: we derive a characteristic propositional-logic formula wM for the input automaton M, in which the variables are pairs of states. Our work is to the best of our knowledge the first in which the bisimulation relation is computed through partition aggregation
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