Search results for "Deterministic automaton"
showing 10 items of 57 documents
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…
Simulation is decidable for one-counter nets
1998
We prove that the simulation preorder is decidable for the class of one-counter nets. A one-counter net consists of a finite-state machine operating on a variable (counter) which ranges over the natural numbers. Each transition can increase or decrease the value of the counter. A transition may not be performed if this implies that the value of the counter becomes negative. The class of one-counter nets is computationally equivalent to the class of Petri nets with one unbounded place, and to the class of pushdown automata where the stack alphabet is restricted to one symbol. To our knowledge, this is the first result in the literature which gives a positive answer to the decidability of sim…
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.
Combinatorics of Finite Words and Suffix Automata
2009
The suffix automaton of a finite word is the minimal deterministic automaton accepting the language of its suffixes. The states of the suffix automaton are the classes of an equivalence relation defined on the set of factors. We explore the relationship between the combinatorial properties of a finite word and the structural properties of its suffix automaton. We give formulas for expressing the total number of states and the total number of edges of the suffix automaton in terms of special factors of the word.
On the Power of Tree-Walking Automata
2000
Tree-walking automata (TWAs) recently received new attention in the fields of formal languages and databases. Towards a better understanding of their expressiveness, we characterize them in terms of transitive closure logic formulas in normal form. It is conjectured by Engelfriet and Hoogeboom that TWAs cannot define all regular tree languages, or equivalently, all of monadic second-order logic. We prove this conjecture for a restricted, but powerful, class of TWAs. In particular, we show that 1-bounded TWAs, that is TWAs that are only allowed to traverse every edge of the input tree at most once in every direction, cannot define all regular languages. We then extend this result to a class …
Regular Varieties of Automata and Coequations
2015
In this paper we use a duality result between equations and coequations for automata, proved by Ballester-Bolinches, Cosme-Ll´opez, and Rutten to characterize nonempty classes of deterministic automata that are closed under products, subautomata, homomorphic images, and sums. One characterization is as classes of automata defined by regular equations and the second one is as classes of automata satisfying sets of coequations called varieties of languages. We show how our results are related to Birkhoff’s theorem for regular varieties.
Deterministic generalized automata
1995
A generalized automaton (GA) is a finite automaton where the single transitions are defined on words rather than on single letters. Generalized automata were considered by K. Hashiguchi who proved that the problem of calculating the size of a minimal GA is decidable.
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.
Non-constructive Methods for Finite Probabilistic Automata
2007
Size (the number of states) of finite probabilistic automata with an isolated cut-point can be exponentially smaller than the size of any equivalent finite deterministic automaton. The result is presented in two versions. The first version depends on Artin's Conjecture (1927) in Number Theory. The second version does not depend on conjectures but the numerical estimates are worse. In both versions the method of the proof does not allow an explicit description of the languages used. Since our finite probabilistic automata are reversible, these results imply a similar result for quantum finite automata.
NON-CONSTRUCTIVE METHODS FOR FINITE PROBABILISTIC AUTOMATA
2008
Size (the number of states) of finite probabilistic automata with an isolated cut-point can be exponentially smaller than the size of any equivalent finite deterministic automaton. However, the proof is non-constructive. The result is presented in two versions. The first version depends on Artin's Conjecture (1927) in Number Theory. The second version does not depend on conjectures not proved but the numerical estimates are worse. In both versions the method of the proof does not allow an explicit description of the languages used. Since our finite probabilistic automata are reversible, these results imply a similar result for quantum finite automata.