Search results for "finite automaton"

Extending formal language hierarchies to higher dimensions

1999

Representation of Autonomous Automata

2001

An autonomous automaton is a finite automaton with output in which the input alphabet has cardinality one when special reduced. We define the transition from automata to semigroups via a representation successful if given two incomparable automata (neither simulate the other), the semigroups representing the automata are distinct. We show that representation by the transition semigroup is not successful. We then consider a representation of automata by semigroups of partial transformations. We show that in general transition from automata to semigroups by this representation is not successful either. In fact, the only successful transition presented is the transiton to this semigroup of par…

Quantum Finite One-Counter Automata

1999

In this paper the notion of quantum finite one-counter automata (QF1CA) is introduced. Introduction of the notion is similar to that of the 2-way quantum finite state automata in [1]. The well-formedness conditions for the automata are specified ensuring unitarity of evolution. A special kind of QF1CA, called simple, that satisfies the well-formedness conditions is introduced. That allows specify rules for constructing such automata more naturally and simpler than in general case. Possible models of language recognition by QF1CA are considered. The recognition of some languages by QF1CA is shown and compared with recognition by probabilistic counterparts.

Complexity of operations on cofinite languages

2010

International audience; We study the worst case complexity of regular operation on cofinite languages (i.e., languages whose complement is finite) and provide algorithms to compute efficiently the resulting minimal automata.

On the Size Complexity of Deterministic Frequency Automata

2013

Austinat, Diekert, Hertrampf, and Petersen [2] proved that every language L that is (m,n)-recognizable by a deterministic frequency automaton such that m > n/2 can be recognized by a deterministic finite automaton as well. First, the size of deterministic frequency automata and of deterministic finite automata recognizing the same language is compared. Then approximations of a language are considered, where a language L′ is called an approximation of a language L if L′ differs from L in only a finite number of strings. We prove that if a deterministic frequency automaton has k states and (m,n)-recognizes a language L, where m > n/2, then there is a language L′ approximating L such that L′ c…

Some Remarks on Automata Minimality

2011

It is well known that the minimization problem of deterministic finite automata (DFAs) is related to the indistinguishability notion of states (cf. [HMU00]). Indeed, a well known technique to minimize a DFA, essentially, consists in finding pairs of states that are equivalent (or indistinguishable), namely pairs of states (p,q) such that it is impossible to assert the difference between p and q only by starting in each of the two states and asking whether or not a given input string leads to a final state. Since, in the testing states equivalence, the notion of initial state is irrelevant, some of the main techniques for the minimization of automata, such as Moore’s algorithm [Moo56] and Ho…

Special factors and the combinatorics of suffix and factor automata

2011

AbstractThe suffix automaton (resp. factor automaton) of a finite word w is the minimal deterministic automaton recognizing the set of suffixes (resp. factors) of w. We study the relationships between the structure of the suffix and factor automata and classical combinatorial parameters related to the special factors of w. We derive formulae for the number of states of these automata. We also characterize the languages LSA and LFA of words having respectively suffix automaton and factor automaton with the minimal possible number of states.

Unary Probabilistic and Quantum Automata on Promise Problems

2015

We continue the systematic investigation of probabilistic and quantum finite automata (PFAs and QFAs) on promise problems by focusing on unary languages. We show that bounded-error QFAs are more powerful than PFAs. But, in contrary to the binary problems, the computational powers of Las-Vegas QFAs and bounded-error PFAs are equivalent to deterministic finite automata (DFAs). Lastly, we present a new family of unary promise problems with two parameters such that when fixing one parameter QFAs can be exponentially more succinct than PFAs and when fixing the other parameter PFAs can be exponentially more succinct than DFAs.

Text Compression Using Antidictionaries

1999

International audience; We give a new text compression scheme based on Forbidden Words ("antidictionary"). We prove that our algorithms attain the entropy for balanced binary sources. They run in linear time. Moreover, one of the main advantages of this approach is that it produces very fast decompressors. A second advantage is a synchronization property that is helpful to search compressed data and allows parallel compression. Our algorithms can also be presented as "compilers" that create compressors dedicated to any previously fixed source. The techniques used in this paper are from Information Theory and Finite Automata.

Quantum Computers and Quantum Automata

2000

Quantum computation is a most challenging project involving research both by physicists and computer scientists. The principles of quantum computation differ from the principles of classical computation very much. When quantum computers become available, the public-key cryptography will change radically. It is no exaggeration to assert that building a quantum computer means building a universal code-breaking machine. Quantum finite automata are expected to appear much sooner. They do not generalize deterministic finite automata. Their capabilities are incomparable.