Search results for "Regular language"
showing 10 items of 54 documents
TWO-DIMENSIONAL FINITE STATE RECOGNIZABILITY
1996
The purpose of this paper is to investigate about a new notion of finite state recognizability for two-dimensional (picture) languages. This notion takes as starting point the characterization of one-dimensional recognizable languages in terms of local languages and projections. Such notion can be extended in a natural way to the two-dimensional case. We first introduce a notion of local picture language and then we define,a recognizable picture language as a projection of a local picture language. The family of recognizable picture languages is denoted by REC. We study some combinatorial and language-theoretic properties of family REC. In particular we prove some closure properties with re…
Nonstochastic languages as projections of 2-tape quasideterministic languages
1998
A language L (n) of n-tuples of words which is recognized by a n-tape rational finite-probabilistic automaton with probability 1-e, for arbitrary e > 0, is called quasideterministic. It is proved in [Fr 81], that each rational stochastic language is a projection of a quasideterministic language L (n) of n-tuples of words. Had projections of quasideterministic languages on one tape always been rational stochastic languages, we would have a good characterization of the class of the rational stochastic languages. However we prove the opposite in this paper. A two-tape quasideterministic language exists, the projection of which on the first tape is a nonstochastic language.
Multi-letter reversible and quantum finite automata
2007
The regular language (a+b)*a (the words in alphabet {a, b} having a as the last letter) is at the moment a classical example of a language not recognizable by a one-way quantum finite automaton (QFA). Up to now, there have been introduced many different models of QFAs, with increasing capabilities, but none of them can cope with this language. We introduce a new, quite simple modification of the QFA model (actually even a deterministic reversible FA model) which is able to recognize this language. We also completely characterise the set of languages recognizable by the new model FAs, by finding a "forbidden construction" whose presence or absence in the minimal deterministic (not necessaril…
Debates with Small Transparent Quantum Verifiers
2014
We study a model where two opposing provers debate over the membership status of a given string in a language, trying to convince a weak verifier whose coins are visible to all. We show that the incorporation of just two qubits to an otherwise classical constant-space verifier raises the class of debatable languages from at most NP to the collection of all Turing-decidable languages (recursive languages). When the verifier is further constrained to make the correct decision with probability 1, the corresponding class goes up from the regular languages up to at least E.
The expressive power of the shuffle product
2010
International audience; There is an increasing interest in the shuffle product on formal languages, mainly because it is a standard tool for modeling process algebras. It still remains a mysterious operation on regular languages.Antonio Restivo proposed as a challenge to characterize the smallest class of languages containing the singletons and closed under Boolean operations, product and shuffle. This problem is still widely open, but we present some partial results on it. We also study some other smaller classes, including the smallest class containing the languages composed of a single word of length 2 which is closed under Boolean operations and shuffle by a letter (resp. shuffle by a l…
On a class of languages with holonomic generating functions
2017
We define a class of languages (RCM) obtained by considering Regular languages, linear Constraints on the number of occurrences of symbols and Morphisms. The class RCM presents some interesting closure properties, and contains languages with holonomic generating functions. As a matter of fact, RCM is related to one-way 1-reversal bounded k-counter machines and also to Parikh automata on letters. Indeed, RCM is contained in L-NFCM but not in L-DFCM, and strictly includes L-CPA. We conjecture that L-DFCM subset of RCM
Efficient learning of regular expressions from good examples
1994
We consider the problem of restoring regular expressions from expressive examples. We define the class of unambiguous regular expressions, the notion of the union number of an expression showing how many union operations can occur directly under any single iteration, and the notion of an expressive example. We present a polynomial time algorithm which tries to restore an unambiguous regular expression from one expressive example. We prove that if the union number of the expression is 0 or 1 and the example is long enough, then the algorithm correctly restores the original expression from one good example. The proof relies on original investigations in theory of covering symbol sequences (wo…
On languages factorizing the free monoid
1996
A language X⊂A* is called factorizing if there exists a language Y⊂A* such that XY = A* This work was partially supported by ESPRIT-EBRA project ASMICS contact 6317 and project 40% MURST “Algoritmi, Modelli di Calcolo e Strutture Informative”. and the product is unambiguous. First we give a combinatorial characterization of factorizing languages. Further we prove that it is decidable whether a regular language X is factorizing and we construct an automaton recognizing the corresponding language Y. For finite languages we show that it suffices to consider words of bounded length. A complete characterization of factorizing languages with three words and explicit regular expression for the co…
The Minimum Amount of Useful Space: New Results and New Directions
2014
We consider minimal space requirements when using memory with restricted access policy (pushdown - hence giving pushdown automata (PDAs), and counter - hence giving counter automata (CAs)) in connection with two-way and realtime head motion. The main results are that: (i) loglogn is a tight space lower bound for accepting general nonregular languages on weak realtime PDAs, (ii) there exist unary nonregular languages accepted by realtime alternating CAs within weak logn space, (iii) there exist nonregular languages accepted by two-way DPADs within strong loglogn space, and, (iv) there exist unary nonregular languages accepted by two-way CAs with quantum and classical states within middle log…
Running time to recognize nonregular languages by 2-way probabilistic automata
1991
R. Freivalds proved that the language {0m1m} can be recognized by 2-way probabilistic finite automata (2pfa) with arbitrarily high probability 1-ɛ. A.G.Greenberg and A.Weiss proved that no 2pfa can recognize this language in expected time \(T(n) = c^\circ{(n)}\). For arbitrary languages C.Dwork and L.Stockmeyer showed somewhat less: if a language L is recognized by a 2pfa in expected time \(T(n) = c^{n^\circ{(1)} }\), then L is regular. First, we improve this theorem replacing the expected time by the time with probability 1-ɛ. On the other hand, time bound by C.Dwork and L.Stockmeyer cannot be improved: for arbitrary k≥2 we exhibit a specific nonregular language that can be recognized by 2…