The projected language of a general deterministic automaton with n states is recognizable by $$2^{n-1} + 2^{n-m} - 1$$ states, where m denotes the number incident to unobservable non-loop transitions, and this bound best possible. Here, we derive tight $$2^{n \lceil \frac{m}{2} \rceil } for permutation automata. For state-partition (also called automata observer property) states. Up now, these,...

1-way quantum finite state automata are reversible in nature, which greatly reduces its accepting property. In fact, the set of languages accepted by 1-way quantum finite automata is a proper subset of regular languages. We introduce 2-tape 1-way quantum finite state automaton (2T1QFA(2))which is a modified version of 1-way 2-head quantum finite state automaton(1QFA(2)). In this paper, we repla...

A model for finite automaton with an open quantum evolution is introduced, and its basic properties are studied. It is shown that the (fuzzy) languages accepted by open evolution quantum automata obey various closure properties. More importantly, it is shown that major other models of finite automata, including probabilistic, measure once quantum, measure many quantum, and Latvian quantum autom...

Typically manipulation of finite automata is performed using their state-transitiongraph (STG) representations. Automata can also be represented using multi-valued networks. Given an automaton, whose next-state function and the set of accepting states are known, consider the network with a single MV latch shown in Figure 1. F is the nextstate logic that depends on the inputs and the current-sta...

Using the methods demonstrated in this paper, a robot with an unknown sensorimotor system can learn sets of features and behaviors adequate to explore a continuous environment and abstract it to a finitestate automaton. The structure of this automaton can then be learned from experience, and constitutes a cognitive map of the environment. A generate-andtest method is used to define a hierarchy ...

The state complexity of a Deterministic Finite-state automaton (DFA) is the number of states in its minimal equivalent DFA. We study the state complexity of random n-state DFAs over a k-symbol alphabet, drawn uniformly from the set [n] × 2 of all such automata. We show that, with high probability, the latter is αkn + O( √ n log n) for a certain explicit constant αk.

We present a symmetric-key predicate-only functional encryption system, SP-FE, which supports functionality for regular languages described by deterministic finite automata. In SP-FE, a data owner can encrypt a string of symbols as encrypted symbols for matching. Later, the data owner can generate predicate tokens of the transitions in a deterministic finite automaton (DFA). The server with the...

We show that for any unambiguous finite automaton with n states there exists an n+1⋅2n/2 recognizes the complement language. This builds and improves upon a similar result by Jirásek et al. (2018) [1]. Our improvement is based on reduction to analysis of problem from extremal graph theory: we vertices, product number its cliques cocliques (independent sets) bounded (n+1)2n.