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Filtrations of Formal Languages by Arithmetic Progressions

Mousavi H., Shallit J.

Fundamenta Informaticae

2013

Vol. 123, nr 2

135--142

A filtration of a formal language L by a sequence s maps L to the set of words formed by taking the letters of words of L indexed only by s. We consider the languages resulting from filtering by all arithmetic progressions. If L is regular, it is easy to see that only finitely many distinct languages result; we give bounds on the number of distinct languages in terms of the state complexity of L. By contrast, there exist CFL’s that give infinitely many distinct languages as a result. We use our technique to show that two related operations, including diag (which extracts the diagonal of words of square length arranged in a square array), preserve regularity but do not preserve context-freeness.

Mirror Images and Schemes for the Maximal Complexity of Nondeterminism

Salomaa A.

Fundamenta Informaticae

2012

Vol. 116, nr 1-4

237-249

We present schemes of deterministic finite automata such that, for every nontrivial automaton A resulting from the scheme with n states, the state complexity of the mirror image of the language L(A) equals 2n. The construction leads to cases, where the increase in complexity is maximal in the transition from nondeterministic devices to deterministic ones. We also discuss the crucial importance of the size of the alphabet and present some open problems.

Extended Shapiro finite state automaton built on DNA

Krasiński T., Sakowski S.

Foundations of Computing and Decision Sciences

2008

Vol. 33, No. 3

241-255

The paper deals with cooperation problems in the case of several parties having different sets of criteria measuring their payoffs. It presents interactive procedures supporting multicriteria analysis and aiding consensus seeking through a mediation process. Using ideas of the cooperative game theory, a mathematical model describing cooperation situations and deriving possible payoffs of parties can be constructed. The model is a base for the analysis made. Solution concepts developed in the cooperative game theory are applied in the mediation process. The procedures can be used in a computer-based system supporting analysis carried on by the parties.

A theoretical model of the Shapiro finite state automaton built on DNA

Krasiński T., Sakowski S.

Theoretical and Applied Informatics

2006

Vol. 18, nr 3

161-174

In the paper a theoretical model (in the form of a splicing system) of a DNA computing machine, constructed in Weizmann Institute of Science by Benenson, Adar, Paz-Elizur, Livneh and Shapiro [4] is given. This splicing system exactly reflects the action of the DNA computer. We describe in detail finite state automaton built on DNA and give its scheme of computation.

W obecnie prowadzonych pracach nad nanosystemami informatyki bada się możliwość wykorzystania DNA do kodowania i przetwarzania informacji. W artykule opracowany jest teoretyczny model (w postaci systemu splatania „splicing system") DNA komputera skonstruowanego w Instytucie Weizmanna przez zespół: Benenson, Adar, Paz-Elizur, Livneh i Shapiro. Model ten dokładnie odzwierciedla działanie tego DNA komputera. Omówiono działanie automatu skończonego opartego na DNA oraz podano jego schemat ideowy działania.

Non-deterministic finite state automata built on DNA

Nowak R., Płucienniczak A.

Prace Naukowe Politechniki Warszawskiej. Elektronika

2006

z. 156

301-308

This paper describes non-deterministic finite-state automaton based on DNA strands. The automaton uses massive parallel processing offered by molecular approach for computation and exhibits a number of advantages over traditional electronic implementations. This device is used to analyze DNA molecules, whether they are described by specified regular expression. Presented ideas are confirmed by experiment performed in genetic engineering laboratory.