Abstract
Finite automata and finite state transducers belong to the bases of (theoretical) computer science with many applications. On the other hand, DNA computing and related bio-inspired paradigms are relatively new fields of computing. Watson–Crick automata are in the intersection of the above fields. These finite automata have two reading heads as they read the upper and lower strands of the input DNA molecule, respectively. In 5′ → 3′ Watson–Crick automata the two reading heads move in the same biochemical direction, that is, from the 5′ end of the strand to the direction of the 3′ end. However, in the double-stranded DNA, the DNA strands are directed in opposite way to each other, therefore 5′ → 3′ Watson–Crick automata read the input from the two extremes. In sensing 5′ → 3′ automata the automata sense if the two heads are at the same position, moreover, the computing process is finished at that time. Based on this class of automata, we define WK transducers such that, at each transition, exactly one input letter is being processed, and exactly one output letter is written on a normal output tape. Some special cases are defined and analyzed,e.g., when only one of the reading heads is being used and when the transducer has only one state. We also show that the minimal transducer is uniquely defined if the transducer is deterministic and it has marked output,i.e., the output letter written in a step identifies the reading head that is used in that transition. We have also used the functions ‘processing order’ and ‘reading heads’ to analyze these transducers.
Highlights
Finite automata and finite state transducers are very basic concepts of theoretical computer science [6, 27]
We mainly focus on deterministic variants. (We note here that, in our previous study [17], we have used the term ‘simple’ for our WK transducers, they were more restricted, since the process went by reading the input letter by letter and to build the output letter by letter, we feel that the term ‘1-limited’ fits, and, in this paper we use this better-fit term.) Since transducers are not about accepting languages, the all-final restriction has no meaning
Transducers with marked output choosing T1 = T and T2 = ∅. This together with Example 3.2 shows that WK transducers and WK transducers with marked output are more powerful than traditional finite state transducers (Mealy and Moore automata)
Summary
Finite automata and finite state transducers are very basic concepts of theoretical computer science [6, 27]. At sensing 5 → 3 WK automata, since exactly one of the strands is read at every pair when the input is fully processed, there is only one usual concept of determinism [20, 22] Based on this fact, we are using the following definition for our WK transducers. The mapping γ that can be defined by a sensing 5 → 3 WK transducer has the property that the prefix of the output depends only on the prefix and the suffix of the input, more formally we have the following theorem. |w1abw2| = n + 1 and γ(w1abw2) = z1x since the deterministic process first proceeds the prefix w1 and the suffix w2 of the input and in state q the letter ab is being read (since one of a and b is λ, ab denotes a string of a sole letter) In this way, z2 = xz and the statement is proven. We show 1-limited 5 → 3 sensing Watson–Crick finite-state transducers with some special properties
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