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In this paper, we investigate the state complexities of (@__ __"i"="1^kL"i)^@__ __ and (@__ __"i"="1^kL"i)^2, where L"i, 1= =2 are regular languages. We establish exact bounds for both of these general combined operations and show that they are much ...

A language L over an alphabet @S is a right (left) ideal if it satisfies L=L@S^* (L=@S^*L). It is a two-sided ideal if L=@S^*L@S^*, and an all-sided ideal if L=@S^*L, the shuffle of @S^* with L. Ideal languages are not only of interest from the ...

In this paper, we continue our study on the state complexity of combined operations on regular languages. We study the state complexities of @?"i"="1^kL"i^2, @?"i"="1^kL"i^2, @?"i"="1^kL"i^R, and @?"i"="1^kL"i^R, for regular languages L"i, 1@?i@?k, k>=...

Tree automata operating on unranked trees use regular languages, called horizontal languages, to define the transitions of the vertical states that define the bottom-up computation of the automaton. It is well known that the deterministic tree automaton ...

The paper determines the number of states in two-way deterministic finite automata (2DFA) over a one-letter alphabet sufficient and in the worst case necessary to represent the results of basic language-theoretic operations on 2DFAs with a certain ...

A transition is unobservable if it is labeled by a symbol removed by a projection. The present paper investigates a new structural property of incomplete deterministic finite automata-a number of states incident with an unobservable transition-and its ...

For each sufficiently large n, there exists a unary regular language L such that both L and its complement Lc are accepted by unambiguous nondeterministic automata with at most n states, while the smallest deterministic automata for these two languages ...

For each sufficiently large n, there exists a unary regular language L such that both L and its complement L ^c are accepted by unambiguous nondeterministic automata with at most n states, while the smallest deterministic automata for these two languages ...

This paper studies the state complexity of (L"1L"2)^R, L"1^RL"2, L"1^*L"2, (L"1@?L"2)L"3, (L"1@?L"2)L"3, L"1L"2@?L"3, and L"1L"2@?L"3 for regular languages L"1, L"2, and L"3. We first show that the upper bound proposed by Liu et al. (2008) [18] for the ...

We consider the state complexity of basic concatenation operations for regular tree languages. We show that the sequential (respectively, parallel) concatenation of tree languages recognized by deterministic bottom-up automata with m and n states can be ...

In this paper, we continue our study on state complexity of combined operations. We study the state complexities of L"1^*@?L"2^*, @?"i"="1^kL"i^*, L"1^*@?L"2^*, and @?"i"="1^kL"i^* for regular languages L"i, 1@?i@?k. We obtain the exact bounds for these ...

Nondeterministic finite automata (NFA) with at most one accepting computation on every input string are known as unambiguous finite automata (UFA). This paper considers UFAs over a one-letter alphabet, and determines the exact number of states in DFAs ...

Profinite topology is used in the classification of rational languages. In particular, several important decidability problems, related to the Malcev product, reduce to the computation of the closure of a rational language in the profinite topology. It ...

We investigate the deterministic and nondeterministic state complexity of languages resulting from the concatenation of two regular languages represented by deterministic and nondeterministic finite automata. We prove that the whole range of ...

We show that if L=NL (the classical logarithmic space classes), then each unary 2nfa (a two-way nondeterministic finite automaton) can be converted into an equivalent 2dfa (a deterministic two-way automaton), keeping the number of states polynomial. (...

Finite automata operating on nested words were introduced by Alur and Madhusudan in 2006. While nested word automata retain many of the desirable properties of ordinary finite automata, there is no known efficient minimization algorithm for ...

We examine questions involving nondeterministic finite automata where all states are final, initial, or both initial and final. First, we prove hardness results for the nonuniversality and inequivalence problems for these NFAs. Next, we characterize the ...

We investigate the descriptional complexity of the nondeterministic finite automaton (NFA) to the deterministic finite automaton (DFA) conversion problem, for automata accepting subregular languages such as combinational languages, definite languages ...

We introduce techniques to prove lower bounds for the number of states needed by finite automata operating on nested words. We study the state complexity of Boolean operations and obtain lower bounds that are tight within an additive constant. The ...

Watson-Crick automata are finite state automata working on double-stranded tapes, introduced to investigate the potential of DNA molecules for computing. In this paper, we continue the investigation of descriptional complexity of Watson-Crick automata ...