Deciding determinism of caterpillar expressions

Deciding determinism of unary languages

In this paper, we investigate the complexity of deciding determinism of unary languages. First, we give a method to derive a set of arithmetic progressions from a regular expression E over a unary alphabet, and establish relations between numbers represented by these arithmetic progressions and words in L(E). Next, we define a problem relating to arithmetic progressions and investigate the comp...

Deterministic Caterpillar Expressions

Checking Determinism of Regular Expressions with Counting

We give characterizations of strong determinism for regular expressions with counting, based on which we present an O(|ΣE ||E|) time algorithm to check whether an expression E with counting is strongly deterministic where ΣE is the set of distinct symbols in E. It improves the previous upper bound of O(|E|) time on the same decision problems for both standard regular expressions and regular exp...

Deciding Determinism of Unary Languages Is coNP-Complete

In this paper, we give the complexity of deciding determinism of unary languages. First, we derive a set of arithmetic progressions from an expression E over a unary alphabet, and give the relations between numbers in these arithmetic progressions and words in L(E). Next, we define a problem related to arithmetic progressions and investigate the complexity of this problem. Finally, by reduction...

Deciding Regular Expressions (In-)Equivalence in Coq

This work presents a mechanically verified implementation of an algorithm for deciding regular expression (in-)equivalence within the Coq proof assistant. This algorithm decides regular expression equivalence through an iterated process of testing the equivalence of their partial derivatives and also does not construct the underlying automata. Our implementation has a refutation step that impro...