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We define a model of advised computation by finite automata where the advice is provided on a separate tape. We consider several variants of the model where the advice is deterministic or randomized, the input tape head is allowed…

We discuss the power and limitation of various "advice," when it is given particularly to weak computational models of one-tape linear-time Turing machines and one-way finite (state) automata. Of various advice types, we consider…

Advice is supplementary information that enhances the computational power of an underlying computation. This paper focuses on advice that is given in the form of a pure quantum state and examines the influence of such advice on the…

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…

We examine inkdots placed on the input string as a way of providing advice to finite automata, and establish the relations between this model and the previously studied models of advised finite automata. The existence of an infinite…

Quantum computing is a new model of computation, based on quantum physics. Quantum computers can be exponentially faster than conventional computers for problems such as factoring. Besides full-scale quantum computers, more restricted…

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…

We realize constant-space quantum computation by measure-many two-way quantum finite automata and evaluate their language recognition power by analyzing patterns of their exotic behaviors and by exploring their structural properties. In…

Advice classes in computational complexity have frequently been used to model real-world scenarios encountered in cryptography, quantum computing and machine learning, where some computational task may be broken down into a preprocessing…

Deterministic synchronous systems consisting of two finite automata running in opposite directions on a shared read-only input are studied with respect to their ability to perform reversible computations, which means that the automata are…

To study relationship between quantum finite automata and probabilistic finite automata, we introduce a notion of probabilistic reversible automata (PRA, or doubly stochastic automata). We find that there is a strong relationship between…

Deterministic one-way time-bounded multi-counter automata are studied with respect to their ability to perform reversible computations, which means that the automata are also backward deterministic and, thus, are able to uniquely step the…

Some of the most interesting and important results concerning quantum finite automata are those showing that they can recognize certain languages with (much) less resources than corresponding classical finite automata…

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…

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…

We study the power of classical and quantum algorithms equipped with nonuniform advice, in the form of a coin whose bias encodes useful information. This question takes on particular importance in the quantum case, due to a surprising…

We prove that endowing a real-time probabilistic or quantum computer with the ability of postselection increases its computational power. For this purpose, we provide a new model of finite automata with postselection, and compare it with…

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…

The question of whether quantum real-time one-counter automata (rtQ1CAs) can outperform their probabilistic counterparts has been open for more than a decade. We provide an affirmative answer to this question, by demonstrating a…

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…