Finite automata and unary languages
Theoretical Computer Science
Intersection and union of regular languages and state complexity
Information Processing Letters
Partial orders on words, minimal elements of regular languages, and state complexity
Theoretical Computer Science
SIAM Journal on Computing
A lower bound technique for the size of nondeterministic finite automata
Information Processing Letters
Algorithmic number theory
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
On the power of Las Vegas for one-way communication complexity, OBDDs, and finite automata
Information and Computation
Communication complexity method for measuring nondeterminism in finite automata
Information and Computation
Communication Complexity and Sequential Compuation
MFCS '97 Proceedings of the 22nd International Symposium on Mathematical Foundations of Computer Science
Randomized Communication Protocols (A Survey)
SAGA '01 Proceedings of the International Symposium on Stochastic Algorithms: Foundations and Applications
STACS '97 Proceedings of the 14th Annual Symposium on Theoretical Aspects of Computer Science
Journal of Automata, Languages and Combinatorics - Third international workshop on descriptional complexity of automata, grammars and related structures
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
Minimizing nfa's and regular expressions
Journal of Computer and System Sciences
State complexity of combined operations
Theoretical Computer Science
On the State Minimization of Nondeterministic Finite Automata
IEEE Transactions on Computers
Finite automata and their decision problems
IBM Journal of Research and Development
On the separation between k-party and (k - 1)-party nondeterministic message complexities
DLT'02 Proceedings of the 6th international conference on Developments in language theory
Descriptional complexity of nondeterministic finite automata
DLT'07 Proceedings of the 11th international conference on Developments in language theory
Inapproximability of nondeterministic state and transition complexity assuming P ≠ NP
DLT'07 Proceedings of the 11th international conference on Developments in language theory
Finding lower bounds for nondeterministic state complexity is hard
DLT'06 Proceedings of the 10th international conference on Developments in Language Theory
Limitations of lower bound methods for deterministic nested word automata
Information and Computation
Hi-index | 5.23 |
In contrast to the minimization of deterministic finite automata (DFA's), the task of constructing a minimal nondeterministic finite automaton (NFA) for a given NFA is PSPACE-complete. Moreover, there are no polynomial approximation algorithms with a constant approximation ratio for estimating the number of states of minimal NFA's. Since one is unable to efficiently estimate the size of a minimal NFA in an efficient way, one should ask at least for developing mathematical proof methods that help to prove good lower bounds on the size of a minimal NFA for a given regular language. Here we consider the robust and most successful lower bound proof technique that is based on communication complexity. In this paper it is proved that even a strong generalization of this method fails for some concrete regular languages. ''To fail'' is considered here in a very strong sense. There is an exponential gap between the size of a minimal NFA and the achievable lower bound for a specific sequence of regular languages. The generalization of the concept of communication protocols is also strong here. It is shown that cutting the input word into 2^O^(^n^^^1^^^/^^^4^) pieces for a size n of a minimal nondeterministic finite automaton and investigating the necessary communication transfer between these pieces as parties of a multiparty protocol does not suffice to get good lower bounds on the size of minimal nondeterministic automata. It seems that for some regular languages one cannot really abstract from the automata model that cuts the input words into particular symbols of the alphabet and reads them one by one using its input head.