Complexity of some natural problems on the class of computable -algebras.
Complexity of the axioms of the alternative set theory
If T is a complete theory stronger than ZF such that axiom of extensionality for classes + T + is consistent for 1 (each alone), where are normal formulae then we show AST + + scheme of choice is consistent. As a consequence we get: there is no proper -formula in AST + scheme of choice. Moreover the complexity of the axioms of AST is studied, e.gẇe show axiom of extensionality is -formula, but not -formula and furthermore prolongation axiom, axioms of choice and cardinalities are -formulae,...
Complexity of the decidability of one class of formulas in quantifier-free set theory with a set-union operator.
Complexity of the decidability of the unquantified set theory with a rank operator.
Complexity results for prefix grammars
Resolving an open problem of Ravikumar and Quan, we show that equivalence of prefix grammars is complete in PSPACE. We also show that membership for these grammars is complete in P (it was known that this problem is in P) and characterize the complexity of equivalence and inclusion for monotonic grammars. For grammars with several premises we show that membership is complete in EXPTIME and hard for PSPACE for monotonic grammars.
Complexity results for prefix grammars
Resolving an open problem of Ravikumar and Quan, we show that equivalence of prefix grammars is complete in PSPACE. We also show that membership for these grammars is complete in P (it was known that this problem is in P) and characterize the complexity of equivalence and inclusion for monotonic grammars. For grammars with several premises we show that membership is complete in EXPTIME and hard for PSPACE for monotonic grammars.
Computability in special models.
Computable categoricity versus relative computable categoricity
We study the notion of computable categoricity of computable structures, comparing it especially to the notion of relative computable categoricity and its relativizations. We show that every 1 decidable computably categorical structure is relatively Δ⁰₂ categorical. We study the complexity of various index sets associated with computable categoricity and relative computable categoricity. We also introduce and study a variation of relative computable categoricity, comparing it to both computable...
Computable families of superatomic Boolean algebras.
Computable solutions of equations over endomorphisms of negative numberings.
Computably rigid models with enumerable submodels.
Computational complexity in algebraic systems.
Computational complexity of a statistical theoremhood testing procedure for propositional calculus with pseudo-random inputs
Computing of graphs of relations using generative grammars
Computing the Rabin index of a parity automaton
Computing the Rabin Index of a Parity Automaton
The Rabin index of a rational language of infinite words given by a parity automaton with n states is computable in time O(n2c) where c is the cardinality of the alphabet. The number of values used by a parity acceptance condition is always greater than the Rabin index and conversely, the acceptance condition of a parity automaton can always be replaced by an equivalent acceptance condition whose number of used values is exactly the Rabin index. This new acceptance condition can also be...
Conditional programmed automata
Congruences parfaites et quasi-parfaites
Conjugacy in monoids.
Consistency proof without transfinite induction for a formal system for turing machines.