Reversible Finite Automata Research Articles

Weakly and Strongly Irreversible Regular Languages

Finite automata whose computations can be reversed, at any point, by knowing the last [Formula: see text] symbols read from the input, for a fixed [Formula: see text], are considered. These devices and their accepted languages are called [Formula: see text]-reversible automata and [Formula: see text]-reversible languages, respectively. The existence of [Formula: see text]-reversible languages which are not [Formula: see text]-reversible is known, for each [Formula: see text]. This gives an infinite hierarchy of weakly irreversible languages, i.e., languages which are [Formula: see text]-reversible for some [Formula: see text]. Conditions characterizing the class of [Formula: see text]-reversible languages, for each fixed [Formula: see text], 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 [Formula: see text]-reversible, but which accepts a [Formula: see text]-reversible language, into an equivalent [Formula: see text]-reversible finite automaton, is presented.

Quotients and atoms of reversible languages

We consider several reversible finite automaton models which have been introduced over decades, and study some properties of their languages. In particular, we look at the question whether the quotients and atoms of a specific class of reversible languages also belong to that class or not. We consider bideterministic automata, reversible deterministic finite automata (REV-DFAs), reversible multiple-entry DFAs (REV-MeDFAs), and several variants of reversible nondeterministic finite automata (REV-NFAs). It is known that the class of REV-DFA languages is strictly included in the class of REV-MeDFA languages. We show that the classes of complete REV-DFA languages and complete REV-MeDFA languages are the same. We also prove that differently from the general case of a REV-DFA language, the minimal DFA for a complete REV-DFA language is a complete REV-DFA. We observe that atoms of any regular language are accepted by REV-NFAs with a single initial and a single final state. We also study atoms of atoms of regular languages and show that any atom of an atom of a regular language is a union of atoms of that language.

Boosting Reversible Pushdown and Queue Machines by Preprocessing

It is well known that reversible finite automata do not accept all regular languages, that reversible pushdown automata do not accept all deterministic context-free languages, and that reversible queue automata are less powerful than deterministic real-time queue automata. It is of significant interest from both a practical and theoretical point of view to close these gaps. We here extend these reversible models by a preprocessing unit which is basically a reversible injective and length-preserving finite state transducer. It turns out that preprocessing the input using such weak devices increases the computational power of reversible deterministic finite automata to the acceptance of all regular languages, whereas for reversible pushdown automata the accepted family of languages lies strictly in between the reversible deterministic context-free languages and the real-time deterministic context-free languages. For reversible queue automata the preprocessing of the input leads to machines that are stronger than real-time reversible queue automata, but less powerful than real-time deterministic (irreversible) queue automata. Moreover, it is shown that the computational power of all three types of machines is not changed by allowing the preprocessing finite state transducer to work irreversibly. Finally, we examine the closure properties of the family of languages accepted by such machines.

One-way reversible multi-head finite automata

One-way multi-head finite automata are considered towards their ability to perform reversible computations. It is shown that, for every number k≥1 of heads, there are problems which can be solved by one-way k-head finite automata, but not by any one-way reversible k-head finite automaton. Additionally, a proper head hierarchy is obtained for one-way reversible multi-head finite automata. Closure properties and decidability problems are investigated as well. It turns out that one-way reversible finite automata with two heads are still a powerful model, since almost all commonly studied problems are not even semidecidable. Finally, descriptional complexity aspects are studied and non-recursive trade-offs are shown.

Reversible Watson–Crick automata

Since 1970, reversible finite automata have generated interest among researcher; but till now, we have not come across a model of reversible read only one-way finite automata which accept all regular languages, In this paper, we introduce a new model of one-way reversible finite automata inspired by the Watson---Crick complementarity relation and show that our model can accept all regular languages. We further show that our model accepts a language which is not accepted by any multi-head deterministic finite automaton.

Exact results for accepting probabilities of quantum automata

One of the properties of the Kondacs–Watrous model of quantum finite automata (QFA) is that the probability of the correct answer for a QFA cannot be amplified arbitrarily. In this paper, we determine the maximum probabilities achieved by QFAs for several languages. In particular, we show that any language that is not recognized by an RFA (reversible finite automaton) can be recognized by a QFA with probability at most 0.7726….

Reversible Finite Automata with Time Redundancy

The possibilities of error detection in discrete devices and of their noise-immunity increase by means of a mathematical model, called a reversible finite automaton with time redundancy, are discussed. The properties and peculiarities of an algorithm for such automata functioning are examined. An example of practical realization is presented.