String Binding-Blocking Automata

In a similar way to DNA hybridization, antibodies which specifically recognize peptide sequences can be used for calculation [3,4]. In [4] the concept of peptide computing via peptide-antibody interaction is introduced and an algorithm to solve the satisfiability problem is given. In [3], (1) it is proved that peptide computing is computationally complete and (2) a method to solve two well-known NP-complete problems namely Hamiltonian path problem and exact cover by 3-set problem (a variation of set cover problem) using the interactions between peptides and antibodies is given. In our earlier paper [1], we proposed a theoretical model called as bindingblocking automata (BBA) for computing with peptide-antibody interactions. In [1] we define two types of transitions leftmost(l) and locally leftmost(ll) of BBA and prove that the acceptance power of multihead finite automata is sandwiched between the acceptance power of BBA in l and ll transitions. In this work we define a variant of binding-blocking automata called as string binding-blocking automata and analyze the acceptance power of the new model. The model of binding-blocking automaton can be informally said as a finite state automaton (reading a string of symbols at a time) with (1) blocking and unblocking functions and (2) priority relation in reading of symbols. Blocking and unblocking facilitates skipping 1 some symbols at some instant and reading it when it is necessary. In the sequel we state some results from [1,2] (1) for every BBA there exists an equivalent BBA without priority, (2) for every language accepted by BBA with l transition, there exists BBA with ll transitions accepting the same language, (3) for every language accepted by BBA with l transition there is an equivalent multi-head finite automata which accepts the same language and (4) for every language L accepted by a multi-head finite automaton there is a language L′ accepted by BBA such that L can be written in the form h−1(L′) where h is a homomorphism from L to L′. The basic model of the string binding-blocking automaton is very similar to a BBA but for the blocking and unblocking. Some string of symbols (starting form the head’s position) can be blocked from being read by the head. So only those symbols which are not already read and not blocked can be read by the head. The finite control of the automaton is divided into three sets of states namely blocking states, unblocking states and general reading states. A read symbol can not be read gain, but a blocked symbol can be unblocked and read.