Category and measure in complexity classes
SIAM Journal on Computing
Relativized topological size of sets of partial recursive functions
Theoretical Computer Science
Almost every set in exponential time is P-bi-immune
Theoretical Computer Science
Effective category and measure in abstract complexity theory
Theoretical Computer Science
Computability, enumerability, unsolvability
Rich omega-Words and Monadic Second-Order Arithmetic
CSL '97 Selected Papers from the11th International Workshop on Computer Science Logic
Resource-bounded Baire category: a stronger approach
SCT '95 Proceedings of the 10th Annual Structure in Complexity Theory Conference (SCT'95)
On the size of sets of computable functions
SWAT '73 Proceedings of the 14th Annual Symposium on Switching and Automata Theory (swat 1973)
Automatic forcing and genericity: on the diagonalization strength of finite automata
DMTCS'03 Proceedings of the 4th international conference on Discrete mathematics and theoretical computer science
Entropy rates and finite-state dimension
Theoretical Computer Science
Automatic forcing and genericity: on the diagonalization strength of finite automata
DMTCS'03 Proceedings of the 4th international conference on Discrete mathematics and theoretical computer science
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Algorithmic and resource-bounded Baire category and corresponding genericity concepts introduced in computability theory and computational complexity theory, respectively, have become elegant and powerful tools in these settings. Here we introduce some new genericity notions based on extension functions computable by finite automata which are tailored for capturing diagonalizations over regular sets and functions. We show that the generic sets obtained either by the partial regular extension functions of any fixed constant length or by all total regular extension of constant length are just the sets with saturated (also called disjunctive) characteristic sequence α. Here a sequence α is saturated if every string occurs in α as a substring. We also show that these automatic generic sets are not regular but may be context free. Furthermore, we introduce stronger automatic genericity notions based on regular extension functions of nonconstant length and we show that the corresponding generic sets are bi-immune for the class of regular and context free languages.