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The Complexity of Membership Problems for Circuits over Sets of Integers
TLDR
There are several membership problems for which the complexity in the case of integers differs significantly from the cases of the natural numbers: Testing membership in the subset of integers produced at the output of a {∪,+,×}-circuit is NEXPTIME-complete, whereas it is PSPACE-complete for the naturalNumbers. Expand
The complexity of membership problems for circuits over sets of integers
TLDR
There are several membership problems for which the complexity in the case of integers differs significantly from the cases of the natural numbers: testing membership in the subset of integers produced at the output of a {∪, +, ×}-circuit is NEXPTIME-complete, whereas it is PSPACE-complete for the naturalNumbers. Expand
Equivalence Problems for Circuits over Sets of Natural Numbers
TLDR
This work gives a systematic characterization of the complexity of equivalence problems over sets of natural numbers and provides an improved upper bound for the case of {∪,∩,−,+,×}-circuits. Expand
Satisfiability of algebraic circuits over sets of natural numbers
TLDR
This work proves that testing satisfiability for {@?,+,x}-circuits is already undecidable, and shows that satisfiability problems capture a wide range of complexity classes such as NL, P, NP, PSPACE, and beyond. Expand
The complexity of unions of disjoint sets
TLDR
It is discovered that such unions of two disjoint NP-complete sets retain much of the complexity of their single components and are complete with respect to more general reducibilities. Expand
Satisfiability of Algebraic Circuits over Sets of Natural Numbers
TLDR
It is proved that testing satisfiability for {∩, +, ×}- circuits already is undecidable, and that in several cases, satisfiability problems are harder than membership problems. Expand
Non-mitotic sets
TLDR
It follows that autoreducibility and mitoticity are not equivalent for all reducibilities between 2-tt and T, although the notions coincide for m- and 1-tt-reducibility. Expand
Equivalence Problems for Circuits over Sets of Natural Numbers
TLDR
This work gives a systematic characterization of the complexity of equivalence problems over sets of natural numbers and provides an improved upper bound for the case of {∪, ∩,-,+, ×}-circuits. Expand
Machines that Can Output Empty Words
TLDR
The e-model for leaf languages which complements the known balanced and unbalanced concepts is proposed, Inspired by the neutral behavior of rejecting paths of NP machines, and allows transducers to output empty words to prove strong gap theorems. Expand
The fault tolerance of NP-hard problems
TLDR
Among other results, the Left-Set technique is used to prove that m-complete sets for NP are nonadaptively weakly deterministically self-correctable while btt- complete sets forNP are weakly DeterministicallySelfCorrectable. Expand
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