ω-automaton

About: ω-automaton is a research topic. Over the lifetime, 2299 publications have been published within this topic receiving 68468 citations. The topic is also known as: stream automaton & ω-automata.

Jumping finite automata

Abstract: The present paper proposes a new investigation area in automata theory — jumping finite automata. These automata work like classical finite automata except that they read input words discontinuously — that is, after reading a symbol, they can jump over some symbols within the words and continue their computation from there. The paper establishes several results concerning jumping finite automata in terms of commonly investigated areas of automata theory, such as decidability and closure properties. Most importantly, it achieves several results that demonstrate differences between jumping finite automata and classical finite automata. In its conclusion, the paper formulates several open problems and suggests future investigation areas.

Efficient learning of typical finite automata from random walks

Abstract: This paper describes new and efficient algorithms for learning deterministic finite automata. Our approach is primarily distinguished by two features: (1) the adoption of an average-case setting to model the ``typical'' labeling of a finite automaton, while retaining a worst-case model for the underlying graph of the automaton, along with (2) a learning model in which the learner is not provided with the means to experiment with the machine, but rather must learn solely by observing the automaton's output behavior on a random input sequence. The main contribution of this paper is in presenting the first efficient algorithms for learning nontrivial classes of automata in an entirely passive learning model. We adopt an on-line learning model in which the learner is asked to predict the output of the next state, given the next symbol of the random input sequence; the goal of the learner is to make as few prediction mistakes as possible. Assuming the learner has a means of resetting the target machine to a fixed start state, we first present an efficient algorithm that article no. IC972648

NFAs with tagged transitions, their conversion to deterministic automata and application to regular expressions

Abstract: A conservative extension to traditional nondeterministic finite automata (NFAs) is proposed to keep track of the positions in the input string for the last uses of selected transitions, by adding "tags" to transitions. The resulting automata are reminiscent of nondeterministic Mealy machines. A formal semantics of automata with tagged transitions is given. An algorithm is given to convert these augmented automata to the corresponding deterministic automata, which can be used to process strings efficiently. The application to regular expressions is discussed, explaining how the algorithms can be used to implement, for example, substring addressing and a lookahead operator, and an informal comparison to other widely-used algorithms is made.

Succinctness of two-way probabilistic and quantum finite automata

Abstract: We introduce a new model of two-way finite automaton, which is endowed with the capability of resetting the position of the tape head to the left end of the tape in a single move during the computation. Several variants of this model are examined, with the following results: The weakest known model of computation where quantum computers recognize more languages with bounded error than their classical counterparts is identified. We prove that two-way probabilistic and quantum finite automata (2PFAs and 2QFAs) can be considerably more concise than both their one-way versions (1PFAs and 1QFAs), and two-way nondeterministic finite automata (2NFAs). For this purpose, we demonstrate several infinite families of regular languages which can be recognized with some fixed probability greater than 1 2 by just tuning the transition amplitudes of a 2QFA (and, in one case, a 2PFA) with a constant number of states, whereas the sizes of the corresponding 1PFAs, 1QFAs and 2NFAs grow without bound. We also show that 2QFAs with mixed states can support highly efficient probability amplification.

Towards Regular Languages over Infinite Alphabets

Abstract: Motivated by formal models recently proposed in the context of XML, we study automata and logics on strings over infinite alphabets. These are conservative extensions of classical automata and logics defining the regular languages on finite alphabets. Specifically, we consider register and pebble automata, and extensions of first-order logic and monadic second-order logic. For each type of automaton we consider one-way and two-way variants, as well as deterministic, non-deterministic, and alternating control. We investigate the expressiveness and complexity of the automata, their connection to the logics, as well as standard decision problems.