With probability one, a random oracle separates PSPACE from the polynomial-time hierarchy
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Random oracles separate PSPACE from the polynomial-time hierarchy
Information Processing Letters
Randomized algorithms
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Data streams: algorithms and applications
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Proceedings of the 12th Colloquium on Automata, Languages and Programming
LATIN '92 Proceedings of the 1st Latin American Symposium on Theoretical Informatics
Probabilistic Approximation of Some NP Optimization Problems by Finite-State Machines
RANDOM '97 Proceedings of the International Workshop on Randomization and Approximation Techniques in Computer Science
Succinct representations of languages by DFA with different levels of reliability
Theoretical Computer Science - Descriptional complexity of formal systems
Tradeoffs between reliability and conciseness of deterministic finite automata
Journal of Automata, Languages and Combinatorics - Special issue: Selected papers of the fourth international workshop on descriptional complexity of formal systems
On the existence of regular approximations
Theoretical Computer Science
Efficient implementation of algorithms for approximate exponentiation
Information Processing Letters
Randomness and the density of hard problems
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
SIAM Journal on Computing
| Hi-index | 0.00 |
Approximate computation is a central concept in algorithms and computation theory. Our notion of approximation is that the algorithm performs correctly on most of the inputs. We propose some finite automata models to study the question of how well a finite automaton can approximately recognize a non-regular language. On the one hand, we show that there are natural problems for which a DFA can correctly solve almost all the instances, but not all instances. An example of such a problem is a decision question about the number of digits in the square of a given integer. On the other hand, we show that some languages (such as L majority = {x ∈ (0 + 1)* | x has more 1′s than 0′s }) can't be approximated by any regular language in a strong sense. We also show that there are problems that are intermediate (between the extremes stated above) in terms of how we well a regular language can approximate it. An example of such a problem is a decision question about the number of digits in the product of two integers. We also present results comparing different models of approximation.