Watson-Crick Jumping Finite Automata

On Regularity of Languages Generated by Copying Systems ; CU-CS-234-82

Abstract: Abstract Let Σ be an arbitrary fixed alphabet. The direct copying relation (over Σ+) is a binary relation defined by: x copy y if and only if x = x1ux2 and y = x1uux2 for some words x1,x2,u where u is nonempty. The copying relation copy∗ is defined as the reflexive and transitive closure of copy. A copying system is an ordered pair G = (Σ, w) where w ϵΣ+; its language is L(G) = {zϵΣ + : w copy ∗ z} , it is referred to as a copy language. This note provides a sufficient condition for a copy language to be regular; an application of this condition is demonstrated.

Generalized Circular One-Way Jumping Finite Automata.

Abstract: A new discontinuous model of computation called one-way jumping finite automata was defined by H. Chigahara et. al. This model was a restricted version of the model jumping finite automata. These automata read an input symbol-by-symbol and jump only in one direction. A generalized linear one-way jumping finite automaton makes jumps after deleting a substring of an input string and then changes its state. These automata can make sequence of jumps in only one direction on an input string either from left to right or from right to left. We show that newly defined model is powerful than its original counterpart. We define and compare the variants, generalized right linear one-way jumping finite automata and generalized left linear one-way jumping finite automata. We also compare the newly defined models with Chomsky hierarchy. Finally, we explore closure properties of the model.

On the Languages Accepted by Watson-Crick Finite Automata with Delays

Abstract: In this work, we analyze the computational power of Watson-Crick finite automata (WKFA) if some restrictions over the transition function in the model are imposed. We consider that the restrictions imposed refer to the maximum length difference between the two input strands which is called the delay. We prove that the language class accepted by WKFA with such restrictions is a proper subclass of the languages accepted by arbitrary WKFA in general. In addition, we initiate the study of the language classes characterized by WKFAs with bounded delays. We prove some of the results by means of various relationships between WKFA and sticker systems.

The String-to-String Correction Problem

Abstract: The string-to-string correction problem is to determine the distance between two strings as measured by the minimum cost sequence of “edit operations” needed to change the one string into the other. The edit operations investigated allow changing one symbol of a string into another single symbol, deleting one symbol from a string, or inserting a single symbol into a string. An algorithm is presented which solves this problem in time proportional to the product of the lengths of the two strings. Possible applications are to the problems of automatic spelling correction and determining the longest subsequence of characters common to two strings.

DNA computing, sticker systems, and universality ?

Abstract: We introduce the sticker systems, a computability model, which is an abstraction of the computations using the Watson-Crick complementarity as in Adleman's DNA computing experiment, [1]. Several types of sticker systems are shown to characterize (modulo a weak coding) the regular languages, hence the power of finite automata. One variant is proven to be equivalent to Turing machines. Another one is found to have a strictly intermediate power.

Jumping finite automata

Abstract: The present paper proposes a new investigation area in automata theory — jumping finite automata. These automata work like classical finite automata except that they read input words discontinuously — that is, after reading a symbol, they can jump over some symbols within the words and continue their computation from there. The paper establishes several results concerning jumping finite automata in terms of commonly investigated areas of automata theory, such as decidability and closure properties. Most importantly, it achieves several results that demonstrate differences between jumping finite automata and classical finite automata. In its conclusion, the paper formulates several open problems and suggests future investigation areas.