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
On the existence of regular approximations
Theoretical Computer Science
On the density of regular and context-free languages
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
Statistical estimation with bounded memory
Statistics and Computing
Approximating deterministic lattice automata
ATVA'12 Proceedings of the 10th international conference on Automated Technology for Verification and Analysis
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Approximate computation is a central concept in algorithms and computation theory. Our notion of approximation is that the algorithm perform 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. The design of these DFA's leads to a linear time randomized algorithm for approximate integer multiplication. On the other hand, we show that some languages (such as Lmajority = {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 present results comparing different models of approximation.