• Publications
  • Influence
Complexity of Constraint Satisfaction Problems over Finite Subsets of Natural Numbers
  • Titus Dose
  • Computer Science, Mathematics
  • Electron. Colloquium Comput. Complex.
  • 2016
TLDR
The computational complexity of constraint satisfaction problems that are based on integer expressions and algebraic circuits, such as L, P, NP, PSPACE, NEXP, and even Sigma_1, the class of c.e. languages, is studied. Expand
Emptiness Problems for Integer Circuits
TLDR
It turns out that the following problems are equivalent to PIT, which shows that the challenge to improve their bounds is just a reformulation of a major open problem in algebraic computing complexity. Expand
NP-Completeness, Proof Systems, and Disjoint NP-Pairs
TLDR
The article investigates the relation between three well-known hypotheses, Hunion, Hopps and Hcpair, and characterizations of Hunion and two variants in terms of coNP-completeness and pproducibility of the set of hard formulas of propositional proof systems are obtained. Expand
An oracle separating conjectures about incompleteness in the finite domain
  • Titus Dose
  • Computer Science, Mathematics
  • Theor. Comput. Sci.
  • 24 February 2020
TLDR
There is no relativizable proof for the implication DisjNP ∧ UP ∧ NP ∩ coNP ⇒ SAT, so an oracle is constructed relative to which Disj NP, ¬ SAT, UP, and NP ∪ coNP hold. Expand
P-Optimal Proof Systems for Each Set in NP but no Complete Disjoint NP-pairs Relative to an Oracle
  • Titus Dose
  • Mathematics, Computer Science
  • ArXiv
  • 11 April 2019
TLDR
An oracle is constructed relative to which no many-one complete disjoint NP-pairs exist and each problem in NP has P-optimal proof systems, showing that there is no relativizable proof for $\mathsf{DisjNP} \Rightarrow \Mathsf{SAT}$. Expand
Balance problems for integer circuits
  • Titus Dose
  • Mathematics, Computer Science
  • Theor. Comput. Sci.
  • 24 December 2019
TLDR
The work shows that the balance problem for { ∖, ⋅ } -circuits is undecidable which is the first natural problem for integer circuits or related constraint satisfaction problems that admits only one arithmetic operation and is proven to be Undecidable. Expand
P≠NP and All Sets in NP∪coNP Have P-Optimal Proof Systems Relative to an Oracle
Balance Problems for Integer Circuits
  • Titus Dose
  • Computer Science, Mathematics
  • Electron. Colloquium Comput. Complex.
  • 2018
TLDR
The work shows that the balance problem for {−, ·}-circuits is undecidable which is the first natural problem for integer circuits or related constraint satisfaction problems that admits only one arithmetic operation and is proven to be Undecidable. Expand
P-Optimal Proof Systems for Each NP-Complete Set but no Complete Disjoint NP-Pairs Relative to an Oracle.
  • Titus Dose
  • Mathematics, Computer Science
  • 1 April 2019
TLDR
An oracle is constructed relative to which there is no relativizable proof for the implication that NP does not contain many-one complete sets that have P-optimal proof systems. Expand
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