Communication complexity hierarchy
Theoretical Computer Science
On measuring nondeterminism in regular languages
Information and Computation
On the relation between ambiguity and nondeterminism in finite automata
Information and Computation
Non-deterministic communication complexity with few witnesses
Journal of Computer and System Sciences
Nondeterministic communication with a limited number of advice bits
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
A comparison of two lower-bound methods for communication complexity
MFCS '94 Selected papers from the 19th international symposium on Mathematical foundations of computer science
Communication complexity and parallel computing
Communication complexity and parallel computing
Communication complexity
STACS '97 Proceedings of the 14th Annual Symposium on Theoretical Aspects of Computer Science
Translating Regular Expressions into Small epsilon-Free Nondeterministic Finite Automata
STACS '97 Proceedings of the 14th Annual Symposium on Theoretical Aspects of Computer Science
Lower Bounds for Computation with Limited Nondeterminism
COCO '98 Proceedings of the Thirteenth Annual IEEE Conference on Computational Complexity
Las Vegas is better than determinism in VLSI and distributed computing (Extended Abstract)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Some complexity questions related to distributive computing(Preliminary Report)
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
Economy of description by automata, grammars, and formal systems
SWAT '71 Proceedings of the 12th Annual Symposium on Switching and Automata Theory (swat 1971)
The Tractability Frontier for NFA Minimization
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
The tractability frontier for NFA minimization
Journal of Computer and System Sciences
On separating constant from polynomial ambiguity of finite automata
SOFSEM'06 Proceedings of the 32nd conference on Current Trends in Theory and Practice of Computer Science
Space- and Time-Bounded Nondeterminism for Cellular Automata
Fundamenta Informaticae - Cellular Automata
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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. Our results are: 1. There is an exponential gap in the number of states between unambiguous nfa's and general nfa's. Moreover, deterministic communication complexity provides lower bounds on the size of unambiguous nfa's. 2. For an nfa A we consider the complexity measures adviceA(n) as the number of advice bits, ambigA(n) as the number of accepting computations, and lea fA(n) as the number of computations for worst case inputs of size n. These measures are correlated as follows (assuming that the nfa A has at most one "terminally rejecting" state): adviceA(n); ambigA(n) ≤ leafA(n) ≤ O(adviceA(n) ċ ambigA(n)). 3. leafA(n) is always either a constant, between linear and polynomial in n, or exponential in n. 4. There is a language for which there is an exponential size gap between nfa's with exponential leaf number/ambiguity and nfa's with polynomial leaf number/ambiguity. There also is a family of languages KONm2 such that there is an exponential size gap between nfa's with polynomial leaf number/ambiguity and nfa's with ambiguity m.