Series-Parallel Automata and Short Regular Expressions

Abstract

Computing short regular expressions equivalent to a given finite automaton is a hard task. In this work we present a class of acyclic automata for which it is possible to obtain in time O(n 2 log n) an equivalent regular expression of size O(n). A characterisation of this class is made using properties of the underlying digraphs that correspond to the series-parallel digraphs class. Using this characterisation we present an algorithm for the generation of automata of this class and an enumerative formula for the underlying digraphs with a given number of vertices.

State Elimination Ordering Strategies: Some Experimental Results

“…Acyclic NFAs for which in each step of the state elimination process there is a state satisfying these conditions were studied by Moreira and Reis [MR09] and called SP-automata. For this class it is possible to obtain a linear size r.e.…”

“…Several exponential lower bounds are provided in the literature [EKSW05,GH08a] showing that the exponential blow-up is unavoidable. For specific classes of automata, better upper bounds can be found [EKSW05,GF08,Sak05,MR09]. In particular, Gruber and Holzer [GH08b] presented an algorithm that converts an n-state deterministic finite automaton (DFA) over a binary alphabet into a regular expression of size at most O(1.742 n ).…”

From Finite Automata to Regular Expressions and Back—A Summary on Descriptional Complexity

“…The conversion problem has been studied also for a few other special cases of finite automata. Examples include finite automata whose underlying digraph is an acyclic series-parallel digraph [88], Thompson digraphs [36], and digraphs induced by Glushkov automata [16].…”