Restricted deterministic Watson-Crick automata

📝 Abstract

In this paper, we introduce a new model of deterministic Watson-Crick automaton namely restricted deterministic Watson- Crick automaton which is a deterministic Watson-Crick automaton where the complementarity string in the lower strand is restricted to a language L. We examine the computational power of the restricted model with respect to L being in different language classes such as regular, unary regular, finite, context free and context sensitive. We also show that computational power of restricted deterministic Watson- Crick automata with L in regular languages is same as that of deterministic Watson-Crick automata and that the set of all languages accepted by restricted deterministic Watson-Crick automata with L in unary regular languages is a proper subset of context free languages.

💡 Analysis

In this paper, we introduce a new model of deterministic Watson-Crick automaton namely restricted deterministic Watson- Crick automaton which is a deterministic Watson-Crick automaton where the complementarity string in the lower strand is restricted to a language L. We examine the computational power of the restricted model with respect to L being in different language classes such as regular, unary regular, finite, context free and context sensitive. We also show that computational power of restricted deterministic Watson- Crick automata with L in regular languages is same as that of deterministic Watson-Crick automata and that the set of all languages accepted by restricted deterministic Watson-Crick automata with L in unary regular languages is a proper subset of context free languages.

📄 Content

Running head: restricted deterministic Watson-Crick automata Title: restricted deterministic Watson-Crick automata

Authors: Kingshuk Chatterjee1, Kumar Sankar Ray(corresponding author)2

Affiliations: 1Electronics and Communication Sciences Unit, Indian Statistical Institute, Kolkata-108

2Professor, Electronics and Communication Sciences Unit, Indian Statistical Institute, Kolkata-108

Address: Electronics and Communication Sciences Unit, Indian Statistical Institute, Kolkata-108.

Telephone Number: +918981074174

Fax Number:033-25776680

Email:ksray@isical.ac.in

Restricted deterministic Watson-Crick automata Kingshuk Chatterjee,1 Kumar Sankar Ray2 Electronics and Communication Science unit, ISI, Kolkata. 1kingshukchaterjee@gmail.com2ksray@isical.ac.in

Abstract: In this paper, we introduce a new model of deterministic Watson-Crick automaton namely restricted deterministic Watson- Crick automaton which is a deterministic Watson-Crick automaton where the complementarity string in the lower strand is restricted to a language L. We examine the computational power of the restricted model with respect to L being in different language classes such as regular, unary regular, finite, context free and context sensitive. We also show that computational power restricted deterministic Watson- Crick automata with L in regular languages is same as that of deterministic Watson-Crick automata and that the set of all languages accepted by restricted deterministic Watson-Crick automata with L in unary regular languages is a proper subset of context free languages. Keywords: non-deterministic Watson-Crick automata, deterministic Watson-Crick automata, restricted automat, regular language, pushdown automata, unary regular languages, context free languages. I. INTRODUCTION Watson-Crick automata [1] are finite automata having two independent heads working on double strands where the characters on the corresponding positions of the two strands are connected by a complementarity relation similar to the Watson-Crick complementarity relation. The movement of the heads although independent of each other is controlled by a single state. Non-deterministic Watson-Crick automata have been explored in [2]. Deterministic Watson-Crick automata and its variants have been explicitly handled in [3]. Parallel Communicating Watson-Crick automata were introduced in [4] and further investigated in [5]. Equivalence of subclasses of two-way Watson-Crick automata is discussed in [6]. A survey of Watson-Crick automata can be found in [7]. Research work regarding state complexity of Watson-Crick automata is reported in [8] and [9].
In this paper, we introduce a new model of deterministic Watson-Crick automata namely restricted deterministic Watson- Crick automata which are deterministic Watson-Crick automata where the complementarity string in the lower strand is restricted to a language L. Thus this restricted automaton can accept a subset of only those strings whose complementarity string is in L. We study the effect of the restriction on the lower strand on the model. We see how the different restriction languages effect the computational power of the restricted deterministic Watson-Crick automata. We show that restricted deterministic Watson-Crick automata with lower strand restricted to regular languages has the same computational power as deterministic Watson-Crick automata. We further show that set of all languages accepted by restricted deterministic Watson- Crick automata with lower strand restricted to unary regular languages is a proper subset of the context free languages. We also examine the computational power of restricted automata where the lower strand is restricted to context free and context sensitive languages.
II. BASIC TERMINOLOGY The symbol V denotes a finite alphabet. The set of all finite words over V is denoted by V*, which includes the empty word λ. The symbol V+=V*- {λ} denotes the set of all non-empty words over the alphabet V. For w ∈ V*, the length of w is denoted by |w|. Let u∈ V* and v ∈V* be two words and if there is some word x ∈ V*, such that v=ux, then u is a prefix of v, denoted by u ≤ v. Two words, u and v are prefix comparable denoted by u~pv if u is a prefix of v or vice versa. A Watson-Crick automaton is a 6-tuple of the form M=(V,ρ,Q,q0,F,δ) where V is an alphabet set, set of states is denoted by Q, ρ ⊆ V×V is the complementarity relation similar to Watson-Crick complementarity relation, q0 is the initial state and F⊆Q is the set of final states. The function δ contains a finite number of transition rules of the form q  →q’, which denotes that the machine in state q parses w1 in upper strand and w2 in lower strand and goes to state q’ where w1, w2∈V*. The symbol   is different from   . While   is just a pair of strings written in that form instead of (w1,w2), the symbol   denotes that the two strands are of

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