We examine the succinctness of one-way, rotating, sweeping, and two-way deterministic finite automata (1dfas, rdfas, sdfas, 2dfas). Here, a sdfa is a 2dfa whose head can change direction only on the endmarkers and a rdfa is a sdfa whose head is reset on the left end of the input every time the right endmarker is read. We introduce a list of language operators and study the corresponding closure...

A framework for the study of periodic behaviour of twoway deterministic finite automata (2DFA) is developed. Computations of 2DFAs are represented by a two-way analogue of transformation semigroups, every element of which describes the behaviour of a 2DFA on a certain string x. A subsemigroup generated by this element represents the behaviour on strings in x. The main contribution of this paper...

We examine the conjecture that no polynomial can upper bound the increase in the number of states when a one-way nondeterministic finite automaton (1nfa) is converted into an equivalent two-way deterministic finite automaton (2dfa). We study the problem of liveness, which admits 1nfas of polynomial size and is known to defy 2dfas of polynomial size if and only if the conjecture is true. We focu...

We describe three regular expression-based methods to characterize as a regular language the language defined by a two-way automaton. The construction methods yield relatively simple techniques to directly construct one-way automata that simulate the behavior of two-way automata. The approaches also offer conceptually uncomplicated alternative equivalence proofs of two-way automata and one-way ...

optimization is an important methodology for activities in planning and design. the transportation designers are able to introduce better projects when they can save time and cost of travel for project by optimization methods. most of the optimization problems in engineering are more complicated than they can be solved by custom optimization methods. the most common and available methods are he...