General Finite Automata Research Articles

A comparison of collapsed Bayesian methods for probabilistic finite automata

This paper describes several collapsed Bayesian methods, which work by first marginalizing out transition probabilities, for inferring several kinds of probabilistic finite automata. The methods include collapsed Gibbs sampling (CGS) and collapsed variational Bayes, as well as two new methods. Their targets range over general probabilistic finite automata, hidden Markov models, probabilistic deterministic finite automata, and variable-length grams. We implement and compare these algorithms over the data sets from the Probabilistic Automata Learning Competition (PAutomaC), which are generated by various types of automata. We report that the CGS-based algorithm designed to target general probabilistic finite automata performed the best for any types of data.

Characterizations of one-way general quantum finite automata

Generally, unitary transformations limit the computational power of quantum finite automata (QFA). In this paper, we study a generalized model named one-way general quantum finite automata (1gQFA), in which each symbol in the input alphabet induces a trace-preserving quantum operation, instead of a unitary transformation. Two different kinds of 1gQFA will be studied: measure-once one-way general quantum finite automata (MO-1gQFA) where a measurement deciding to accept or reject is performed at the end of a computation, and measure-many one-way general quantum finite automata (MM-1gQFA) where a similar measurement is performed after each trace-preserving quantum operation on reading each input symbol. We characterize the measure-once model from three aspects: the closure property, the language recognition power, and the equivalence problem. We prove that MO-1gQFA recognize, with bounded error, precisely the set of all regular languages. Our results imply that some models of quantum finite automata proposed in the literature, which were expected to be more powerful, still cannot recognize non-regular languages. We prove that MM-1gQFA also recognize only regular languages with bounded error. Thus, MM-1gQFA and MO-1gQFA have the same language recognition power, in sharp contrast with traditional MO-1QFA and MM-1QFA, the former being strictly less powerful than the latter. Finally, we present a necessary and sufficient condition for two MM-1gQFA to be equivalent.

Constructing finite automata with invertibility by transformation method

R a ,R b transformations were successfully applied to establish invertibility theory for linear and quasi-linear finite automata over finite fields. In a previous paper, the authors generalizedR a ,R b transformations to deal with nonlinear memory finite automata, and gave sufficient conditions for weak inverse and for weakly invertible memory finite automata and inversion processes concerned; methods by transformation to generate a kind of nonlinear memory finite automata satisfying one of these sufficient conditions were also given. This paper extends the concepts, methods and results to general finite automata, in which states consist of finite input history, finite output history and finite “inner state” history.