Parallel communicating one-way reversible finite automata system

In this paper, we discuss the computational power of parallel communicating finite automata system with 1-way reversible finite automaton as components. We show that unlike the multi-head one way reversible finite automata model (where we are still not sure whether it accepts all the regular languages) parallel communicating one-way reversible finite automata systems can accept all the regular languages. Moreover for every multi-head one way reversible finite automaton there exist a parallel communicating one-way reversible finite automata system which accepts the same language. We also make an interesting observation that although the components of the system are reversible the system as a whole is not reversible. On the basis of which we conjecture that parallel communicating one-way reversible finite automata systems may accept languages not accepted by multi-head one way reversible finite automata

Weakly and Strongly Irreversible Regular Languages

Finite automata whose computations can be reversed, at any point, by knowing the last k symbols read from the input, for a fixed k, are considered. These devices and their accepted languages are called k-reversible automata and k-reversible languages, respectively. The existence of k-reversible languages which are not (k-1)-reversible is known, for each k>1. This gives an infinite hierarchy of weakly irreversible languages, i.e., languages which are k-reversible for some k. Conditions characterizing the class of k-reversible languages, for each fixed k, and the class of weakly irreversible languages are obtained. From these conditions, a procedure that given a finite automaton decides if the accepted language is weakly or strongly (i.e., not weakly) irreversible is described. Furthermore, a construction which allows to transform any finite automaton which is not k-reversible, but which accepts a k-reversible language, into an equivalent k-reversible finite automaton, is presented.Comment: In Proceedings AFL 2017, arXiv:1708.0622

Reversible Languages Having Finitely Many Reduced Automata

Reversible forms of computations are often interesting from an energy efficiency point of view. When the computation device in question is an automaton, it is known that the minimal reversible automaton recognizing a given language is not necessarily unique, moreover, there are languages having arbitrarily large reversible recognizers possessing no nontrivial reversible congruence. However, the exact characterization of this class of languages was open. In this paper we give a forbidden pattern capturing the reversible regular languages having only finitely many reduced reversible automata, allowing an efficient (NL) decision procedure.Comment: In Proceedings AFL 2017, arXiv:1708.0622

Reversible Watson-Crick Automata

Watson-Crick automata are finite automata working on double strands. Extensive research work has already been done on non-deterministic Watson-Crick automata and on deterministic Watson-Crick automata. In this paper, we introduce a new model of Watson-Crick automata which is reversible in nature named reversible Watson-Crick automata and explore its computational power. We show even though the model is reversible and one way it accepts all regular languages and also analyze the state complexity of the above stated model with respect to non-deterministic block automata and non-deterministic finite automata and establish its superiority. We further explore the relation of the reversible model with twin-shuffle language and recursively enumerable languages.Comment: arXiv admin note: text overlap with arXiv:1507.0528

State Complexity of Reversible Watson-Crick Automata

Reversible Watson-Crick automata introduced by Chatterjee et.al. is a reversible variant of an Watson-Crick automata. It has already been shown that the addition of DNA properties to reversible automata significantly increases the computational power of the model. In this paper, we analyze the state complexity of Reversible Watson-Crick automata with respect to non-deterministic finite automata. We show that Reversible Watson-Crick automata in spite of being reversible in nature enjoy state complexity advantage over non deterministic finite automata. The result is interesting because conversion from non deterministic to deterministic automata results in exponential blow up of the number of states and classically increase in number of heads of the automata cannot compensate for non-determinism in deterministic and reversible models

Quantum Finite Automata and Probabilistic Reversible Automata: R-trivial Idempotent Languages

We study the recognition of R-trivial idempotent (R1) languages by various models of "decide-and-halt" quantum finite automata (QFA) and probabilistic reversible automata (DH-PRA). We introduce bistochastic QFA (MM-BQFA), a model which generalizes both Nayak's enhanced QFA and DH-PRA. We apply tools from algebraic automata theory and systems of linear inequalities to give a complete characterization of R1 languages recognized by all these models. We also find that "forbidden constructions" known so far do not include all of the languages that cannot be recognized by measure-many QFA.Comment: 30 pages, 3 figure

1-way quantum finite automata: strengths, weaknesses and generalizations

We study 1-way quantum finite automata (QFAs). First, we compare them with their classical counterparts. We show that, if an automaton is required to give the correct answer with a large probability (over 0.98), then the power of 1-way QFAs is equal to the power of 1-way reversible automata. However, quantum automata giving the correct answer with smaller probabilities are more powerful than reversible automata. Second, we show that 1-way QFAs can be very space-efficient. Namely, we construct a 1-way QFA which is exponentially smaller than any equivalent classical (even randomized) finite automaton. This construction may be useful for design of other space-efficient quantum algorithms. Third, we consider several generalizations of 1-way QFAs. Here, our goal is to find a model which is more powerful than 1-way QFAs keeping the quantum part as simple as possible.Comment: 23 pages LaTeX, 1 figure, to appear at FOCS'9

Two-way Quantum One-counter Automata

After the first treatments of quantum finite state automata by Moore and Crutchfield and by Kondacs and Watrous, a number of papers study the power of quantum finite state automata and their variants. This paper introduces a model of two-way quantum one-counter automata (2Q1CAs), combining the model of two-way quantum finite state automata (2QFAs) by Kondacs and Watrous and the model of one-way quantum one-counter automata (1Q1CAs) by Kravtsev. We give the definition of 2Q1CAs with well-formedness conditions. It is proved that 2Q1CAs are at least as powerful as classical two-way deterministic one-counter automata (2D1CAs), that is, every language L recognizable by 2D1CAs is recognized by 2Q1CAs with no error. It is also shown that several non-context-free languages including {a^n b^{n^2}} and {a^n b^{2^n}} are recognizable by 2Q1CAs with bounded error.Comment: LaTeX2e, 14 pages, 3 figure

Watson-Crick Quantum Finite Automata

1-way quantum finite automata are deterministic and reversible in nature, which greatly reduces its accepting property. In fact the set of languages accepted by 1-way quantum finite automata is a proper subset of regular languages. In this paper we replace the tape head of 1-way quantum finite automata with DNA double strand and name the model Watson-Crick quantum finite automata. The non-injective complementarity relation of Watson-Crick automata introduces non-determinism in the quantum model. We show that this introduction of non-determinism increases the computational power of 1-way Quantum finite automata significantly. We establish that Watson-Crick quantum finite automata can accept all regular languages and that it also accepts some languages not accepted by any multihead deterministic finite automata. Exploiting the superposition property of quantum finite automata we show that Watson-Crick quantum finite automata accept the language L=ww where w belongs to {a,b}*

2-tape 1-way Quantum Finite State Automata

1-way quantum finite state automata are reversible in nature, which greatly reduces its accepting property. In fact, the set of languages accepted by 1-way quantum finite automata is a proper subset of regular languages. We introduce 2-tape 1-way quantum finite state automaton (2T1QFA(2))which is a modified version of 1-way 2-head quantum finite state automaton(1QFA(2)). In this paper, we replace the single tape of 1-way 2-head quantum finite state automaton with two tapes. The content of the second tape is determined using a relation defined on input alphabet. The main claims of this paper are as follows: (1)We establish that 2-tape 1-way quantum finite state automaton(2T1QFA(2)) can accept all regular languages (2)A language which cannot be accepted by any multi-head deterministic finite automaton can be accepted by 2-tape 1-way quantum finite state automaton(2T1QFA(2)) .(3) Exploiting the superposition property of quantum automata we show that 2-tape 1-way quantum finite state automaton(2T1QFA(2)) can accept the language L=ww