On measuring nondeterminism in regular languages
Information and Computation
On the state complexity of intersection of regular languages
ACM SIGACT News
On the relation between ambiguity and nondeterminism in finite automata
Information and Computation
The state complexities of some basic operations on regular languages
Theoretical Computer Science
Handbook of formal languages, vol. 1
NFA to DFA transformation for finite languages over arbitrary alphabets
Journal of Automata, Languages and Combinatorics
State complexity of regular languages
Journal of Automata, Languages and Combinatorics
Minimal cover-automata for finite languages
Theoretical Computer Science
Optimal Simulations Between Unary Automata
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
State Complexity of Basic Operations on Finite Languages
WIA '99 Revised Papers from the 4th International Workshop on Automata Implementation
Economy of description by automata, grammars, and formal systems
SWAT '71 Proceedings of the 12th Annual Symposium on Switching and Automata Theory (swat 1971)
Introduction to Automata Theory, Languages, and Computation
Introduction to Automata Theory, Languages, and Computation
On the descriptional complexity of finite automata with modified acceptance conditions
Theoretical Computer Science - Descriptional complexity of formal systems
State complexity of some operations on binary regular languages
Theoretical Computer Science - Descriptional complexity of formal systems
State complexity of shuffle on trajectories
Journal of Automata, Languages and Combinatorics - Special issue: Selected papers of the fourth international workshop on descriptional complexity of formal systems
Finite-State Registered Automata for Non-Concatenative Morphology
Computational Linguistics
State Complexity: Recent Results and Open Problems
Fundamenta Informaticae - Contagious Creativity - In Honor of the 80th Birthday of Professor Solomon Marcus
Synchronized Shuffle on Backbones
Fundamenta Informaticae - SPECIAL ISSUE ON TRAJECTORIES OF LANGUAGE THEORY Dedicated to the memory of Alexandru Mateescu
State complexity of combined operations
Theoretical Computer Science
On the average state and transition complexity of finite languages
Theoretical Computer Science
Finite-State Technology as a Programming Environment
CICLing '07 Proceedings of the 8th International Conference on Computational Linguistics and Intelligent Text Processing
Descriptional and Computational Complexity of Finite Automata
LATA '09 Proceedings of the 3rd International Conference on Language and Automata Theory and Applications
Proceedings of the twenty-eighth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Unary language operations and their nondeterministic state complexity
DLT'02 Proceedings of the 6th international conference on Developments in language theory
State complexity of catenation combined with union and intersection
CIAA'10 Proceedings of the 15th international conference on Implementation and application of automata
Journal of Computer and System Sciences
State complexity of four combined operations composed of union, intersection, star and reversal
DCFS'11 Proceedings of the 13th international conference on Descriptional complexity of formal systems
Lower bounds for complementation of ω-automata via the full automata technique
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
Size complexity of rotating and sweeping automata
Journal of Computer and System Sciences
On the state complexity of combined operations
CIAA'06 Proceedings of the 11th international conference on Implementation and Application of Automata
Complexity of operations on cofinite languages
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
State complexity of concatenation and complementation of regular languages
CIAA'04 Proceedings of the 9th international conference on Implementation and Application of Automata
CIAA'04 Proceedings of the 9th international conference on Implementation and Application of Automata
State complexity of union and intersection of star on k regular languages
Theoretical Computer Science
State complexity of combined operations with two basic operations
Theoretical Computer Science
State complexity of star and square of union of k regular languages
DCFS'12 Proceedings of the 14th international conference on Descriptional Complexity of Formal Systems
Synchronized Shuffle on Backbones
Fundamenta Informaticae - SPECIAL ISSUE ON TRAJECTORIES OF LANGUAGE THEORY Dedicated to the memory of Alexandru Mateescu
State complexity of union and intersection of square and reversal on k regular languages
Theoretical Computer Science
State Complexity: Recent Results and Open Problems
Fundamenta Informaticae - Contagious Creativity - In Honor of the 80th Birthday of Professor Solomon Marcus
State Complexity of Combined Operations with Union, Intersection, Star and Reversal
Fundamenta Informaticae - Words, Graphs, Automata, and Languages; Special Issue Honoring the 60th Birthday of Professor Tero Harju
Descriptional complexity of determinization and complementation for finite automata
CATS '11 Proceedings of the Seventeenth Computing: The Australasian Theory Symposium - Volume 119
Descriptional complexity of determinization and complementation for finite automata
CATS 2011 Proceedings of the Seventeenth Computing on The Australasian Theory Symposium - Volume 119
State complexity of star of union and square of union on k regular languages
Theoretical Computer Science
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The state complexities of basic operations on nondeterministic finite automata (NFA) are investigated. In particular, we consider Boolean operations, catenation operations - concatenation, iteration, λ-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 complementation tight bounds in the order of magnitude are proved. It turns out that the state complexities of operations on NFAs and deterministic finite automata (DFA) are quite different. For example, the reversal and concatenation have exponential state complexity on DFAs but linear complexity on NFAs. Conversely, the complementation can be done with linear complexity on DFAs but needs exponentially many states on NFAs.