Search results for "Probabilistic automaton"
showing 10 items of 25 documents
Arithmetical Analysis of Biomolecular Finite Automaton
2013
In the paper we present a theoretical analysis of extension of the finite automaton built on DNA (introduced by the Shapiro team) to an arbitrary number of states and symbols. In the implementation we use a new idea of several restriction enzymes instead of one. We give arithmetical conditions for the existence of such extensions in terms of ingredients used in the implementation.
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…
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…
Weak and strong recognition by 2-way randomized automata
1997
Languages weakly recognized by a Monte Carlo 2-way finite automaton with n states are proved to be strongly recognized by a Monte Carlo 2-way finite automaton with no(n) states. This improves dramatically over the previously known result by M.Karpinski and R.Verbeek [10] which is also nontrivial since these languages can be nonregular [5]. For tally languages the increase in the number of states is proved to be only polynomial, and these languages are regular.
On the determinization of weighted finite automata
1998
We study determinization of weighted finite-state automata (WFAs), which has important applications in automatic speech recognition (ASR). We provide the first polynomial-time algorithm to test for the twins property, which determines if a WFA admits a deterministic equivalent. We also provide a rigorous analysis of a determinization algorithm of Mohri, with tight bounds for acyclic WFAs. Given that WFAs can expand exponentially when determinized, we explore why those used in ASR tend to shrink. The folklore explanation is that ASR WFAs have an acyclic, multi-partite structure. We show, however, that there exist such WFAs that always incur exponential expansion when determinized. We then in…
On a class of languages recognizable by probabilistic reversible decide-and-halt automata
2009
AbstractWe analyze the properties of probabilistic reversible decide-and-halt automata (DH-PRA) and show that there is a strong relationship between DH-PRA and 1-way quantum automata. We show that a general class of regular languages is not recognizable by DH-PRA by proving that two “forbidden” constructions in minimal deterministic automata correspond to languages not recognizable by DH-PRA. The shown class is identical to a class known to be not recognizable by 1-way quantum automata. We also prove that the class of languages recognizable by DH-PRA is not closed under union and other non-trivial Boolean operations.
The Complexity of Probabilistic versus Quantum Finite Automata
2002
We present a language Ln which is recognizable by a probabilistic finite automaton (PFA) with probability 1 - ? for all ? > 0 with O(log2 n) states, with a deterministic finite automaton (DFA) with O(n) states, but a quantum finite automaton (QFA) needs at least 2?(n/log n) states.
Finite State Verifiers with Constant Randomness
2012
We give a new characterization of NL as the class of languages whose members have certificates that can be verified with small error in polynomial time by finite state machines that use a constant number of random bits, as opposed to its conventional description in terms of deterministic logarithmic-space verifiers. It turns out that allowing two-way interaction with the prover does not change the class of verifiable languages, and that no polynomially bounded amount of randomness is useful for constant-memory computers when used as language recognizers, or public-coin verifiers.
Regularity of one-letter languages acceptable by 2-way finite probabilistic automata
1991
R. Freivalds proved that the nonregular language {0m1m} can be recognized by 2-way probabilistic finite automata (2pfa) with arbitrarily high probability 1-e (e>0). We prove that such an effect is impossible for one-letter languages: every one-letter language acceptable by 2pfa with an isolated cutpoint is regular.