The state complexities of basic operations on nondeterministic finite automata (NFA) are investigated. In particular, we consider Boolean operations, catenation operations -- concatenation, iteration, -free iteration -- and the reversal on NFAs that accept finite and infinite languages over arbitrary alphabets. Most of the shown bounds are tight in the exact number of states, i.e. the number is sufficient and necessary in the worst case. For the intersection of finite languages and the complementation tight bounds in the order of magnitude are proved.

. We study determinization of weighted finite-state automata (WFAs), which has important applications in automatic speech recognition (ASR). We provide the first polynomial-time algorithm to test for the twins property, which determines if a WFA admits a deterministic equivalent. We also provide a rigorous analysis of a determinization algorithm of Mohri, with tight bounds for acyclic WFAs. Given that WFAs can expand exponentially when determinized, we explore why those used in ASR tend to shrink. The folklore explanation is that ASR WFAs have an acyclic, multi-partite structure. We show, however, that there exist such WFAs that always incur exponential expansion when determinized. We then introduce a class of WFAs, also with this structure, whose expansion depends on the weights: some weightings cause them to shrink, while others, including random weightings, cause them to expand exponentially. We provide experimental evidence that ASR WFAs exhibit this weight dependence. ...

this paper, we present the topological approach to the limitedness problem on distance automata. Our techniques has been improved so that the Brown's result is no longer needed. The main mathematical tools used are the local structure theory for nite semigroup [13] and some basic topological ideas. Most of the technical results in this paper except Lemma 3.9 and Lemma 3.10 were obtained in ([14], [15]). Besides for the sake of completeness, we include all the proofs because many of them have been re-worked for better presentations

While deterministic finite automata seem to be well understood, surprisingly many important problems concerning nondeterministic finite automata (nfa's) remain open. One such problem

While deterministic finite automata seem to be well understood, surprisingly many important problems concerning nondeterministic finite automata (nfa's) remain open. One such problem area is the study of different measures of nondeterminism in finite automata and the estimation of the sizes of minimal nondeterministic finite automata. In this paper the concept of communication complexity is applied in order to achieve progress in this problem area. The main results are as follows: 1. Deterministic communication complexity provides lower bounds on the size of unambiguous nfa's. Applying this fact, the proofs of several results about nfa's with limited ambiguity can be simplified. 2. For an nfa A we consider the complexity measures advice_A(n) as the number of advice bits, ambig_A(n) as the number of accepting computations, and leaf_A(n) as the number of computations for worst case inputs of size n. These measures are correlated as follows (assuming that the nfa A is minimal): advice_A(n), ambig_A(n) lower-equal leaf_A(n) lower-equal O(advice_A(n) times ambig_A(n)). 3. leaf_A(n) is always either a constant, between linear and polynomial in n, or exponential in n. 4. There is a family of languages KON_{k^2} with an exponential size gap between nfa's with polynomial leaf number/ambiguity and nfa's with ambiguity k. This partially provides an answer to the open problem posed by Ravikumar and Ibarra [SIAM J. Comput. 18 (1989), 1263--1282], and Hing Leung [SIAM J. Comput. 27 (1998), 1073--1082]. Keywords: finite automata, nondeterminism, limited ambigiuty, descriptional complexity, communication complexity

Restarting automata can be seen as analytical variants of classical automata as well as of regulated rewriting systems. We study a measure for the degree of nondeterminism of (context-free) languages in terms of deterministic restarting automata that are (strongly) lexicalized. This measure is based on the number of auxiliary symbols (categories)

2 Scientific Work