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The Computational Complexity of Universality Problems for Prefixes, Suffixes, Factors, and Subwords of Regular Languages

Rampersad N., Shallit J., Xu Z.

Fundamenta Informaticae

2012

Vol. 116, nr 1-4

223-236

In this paper we consider the computational complexity of the following problems: given a DFA or NFA representing a regular language L over a finite alphabet Σ, is the set of all prefixes (resp., suffixes, factors, subwords) of all words of L equal to Σ*? In the case of testing universality for factors of languages, there is a connection to two classic problems: the synchronizing words problem of Černy, and Restivo's conjecture on the minimal uncompletable word.

Solving a PSPACE-Complete Problem by Recognizing P Systems with Restricted Active Membranes

Alhazov A., Martin-Vide C., Pan L.

Fundamenta Informaticae

2003

Vol. 58, nr 2

67--77

P systems are parallel molecular computing models based on processing multisets of objects in cell-like membrane structures. Recently, Petr Sosík has shown that a semi-uniform family of P systems with active membranes and 2-division is able to solve the PSPACE-complete problem QBF-SAT in linear time; he has also conjectured that the membrane dissolving rules of the (d) type may be omitted, but probably not the (f) type rules for non-elementary membrane division. In this paper, we partially confirm the conjecture proving that dissolving rules are not necessary. Moreover, the construction is now uniform. It still remains open whether or not non-elementary membrane division is needed.