Search results for "DEVICES"
showing 10 items of 615 documents
Unary Languages Recognized by Two-Way One-Counter Automata
2014
A two-way deterministic finite state automaton with one counter (2D1CA) is a fundamental computational model that has been examined in many different aspects since sixties, but we know little about its power in the case of unary languages. Up to our knowledge, the only known unary nonregular languages recognized by 2D1CAs are those formed by strings having exponential length, where the exponents form some trivial unary regular language. In this paper, we present some non-trivial subsets of these languages. By using the input head as a second counter, we present simulations of two-way deterministic finite automata with linearly bounded counters and linear–space Turing machines. We also show …
Superiority Of One-Way And Realtime Quantum Machines
2012
In automata theory, quantum computation has been widely examined for finite state machines, known as quantum finite automata (QFAs), and less attention has been given to QFAs augmented with counters or stacks. In this paper, we focus on such generalizations of QFAs where the input head operates in one-way or realtime mode, and present some new results regarding their superiority over their classical counterparts. Our first result is about the nondeterministic acceptance mode: Each quantum model architecturally intermediate between realtime finite state automaton and one-way pushdown automaton (one-way finite automaton, realtime and one-way finite automata with one-counter, and realtime push…
Implications of quantum automata for contextuality
2014
We construct zero error quantum finite automata (QFAs) for promise problems which cannot be solved by bounded error probabilistic finite automata (PFAs). Here is a summary of our results: There is a promise problem solvable by an exact two way QFA in exponential expected time but not by any bounded error sublogarithmic space probabilistic Turing machine (PTM). There is a promise problem solvable by an exact two way QFA in quadratic expected time but not by any bounded error o(loglogn) space PTMs in polynomial expected time. The same problem can be solvable by a one way Las Vegas (or exact two way) QFA with quantum head in linear (expected) time. There is a promise problem solvable by a Las …
Improved constructions of quantum automata
2008
We present a simple construction of quantum automata which achieve an exponential advantage over classical finite automata. Our automata use \frac{4}{\epsilon} \log 2p + O(1) states to recognize a language that requires p states classically. The construction is both substantially simpler and achieves a better constant in the front of \log p than the previously known construction of Ambainis and Freivalds (quant-ph/9802062). Similarly to Ambainis and Freivalds, our construction is by a probabilistic argument. We consider the possibility to derandomize it and present some results in this direction.
Nondeterministic Moore automata and Brzozowski's minimization algorithm
2012
AbstractMoore automata represent a model that has many applications. In this paper we define a notion of coherent nondeterministic Moore automaton (NMA) and show that such a model has the same computational power of the classical deterministic Moore automaton. We consider also the problem of constructing the minimal deterministic Moore automaton equivalent to a given NMA. We propose an algorithm that is a variant of Brzozowski’s minimization algorithm in the sense that it is essentially structured as reverse operation and subset construction performed twice. Moreover, we explore more general classes of NMA and analyze the applicability of the algorithm. For some of such classes the algorith…
Standard Sturmian words and automata minimization algorithms
2015
The study of some close connections between the combinatorial properties of words and the performance of the automata minimization process constitutes the main focus of this paper. These relationships have been, in fact, the basis of the study of the tightness and the extremal cases of Hopcroft's algorithm, that is, up to now, the most efficient minimization method for deterministic finite state automata. Recently, increasing attention has been paid to another minimization method that, unlike the approach proposed by Hopcroft, is not based on refinement of the set of states of the automaton, but on automata operations such as determinization and reverse, and is also applicable to non-determ…
Group Input Machine
2009
We introduce a new type of internal memory for finite automata and real-time automata. Instead of using tapes with a prescribed Euclidean structure (one-dimensional or two-dimensional tapes) we allow arbitrary group structure of the internal memory of the automata.
Extremal minimality conditions on automata
2012
AbstractIn this paper we investigate the minimality problem of DFAs by varying the set of final states. In other words, we are interested on how the choice of the final states can affect the minimality of the automata. The state-pair graph is a useful tool to investigate such a problem. The choice of a set of final states for the automaton A defines a coloring of the closed components of the state-pair graph and the minimality of A corresponds to a property of these colored components. A particular attention is devoted to the analysis of some extremal cases such as, for example, the automata that are minimal for any choice of the subset of final states F from the state set Q of the automato…
Automata with Extremal Minimality Conditions
2010
It is well known that the minimality of a deterministic finite automaton (DFA) depends on the set of final states. In this paper we study the minimality of a strongly connected DFA by varying the set of final states. We consider, in particular, some extremal cases. A strongly connected DFA is called uniformly minimal if it is minimal, for any choice of the set of final states. It is called never-minimal if it is not minimal, for any choice of the set of final states. We show that there exists an infinite family of uniformly minimal automata and that there exists an infinite family of never-minimal automata. Some properties of these automata are investigated and, in particular, we consider t…
A graph theoretic approach to automata minimality
2012
AbstractThe paper presents a graph-theoretic approach to test the minimality of a deterministic automaton. In particular, we focus on problems concerning the dependence of the minimality of an automaton on the choice of the set F of final states or on the cardinality of the set F. We introduce different minimality conditions of an automaton and show that such conditions can be characterized in graph-theoretic terms.