# An oracle separating conjectures about incompleteness in the finite domain

@article{Dose2020AnOS, title={An oracle separating conjectures about incompleteness in the finite domain}, author={Titus Dose}, journal={Theor. Comput. Sci.}, year={2020}, volume={809}, pages={466-481} }

Abstract Pudlak [19] lists several major complexity theoretic conjectures relevant to proof complexity and asks for oracles that separate pairs of corresponding relativized conjectures. Among these conjectures are: • DisjNP : The class of all disjoint NP-pairs does not have many-one complete problems. • SAT : NP does not contain many-one complete sets that have P-optimal proof systems. • UP : UP does not have many-one complete problems. • NP ∩ coNP : NP ∩ coNP does not have many-one complete… Expand

#### Topics from this paper

#### 2 Citations

NP-Completeness, Proof Systems, and Disjoint NP-Pairs

- Mathematics, Computer Science
- Electron. Colloquium Comput. Complex.
- 2019

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

Further oracles separating conjectures about incompleteness in the finite domain

- Computer Science
- Theor. Comput. Sci.
- 2020

#### References

SHOWING 1-10 OF 18 REFERENCES

NP-Completeness, Proof Systems, and Disjoint NP-Pairs

- Mathematics, Computer Science
- Electron. Colloquium Comput. Complex.
- 2019

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

INCOMPLETENESS IN THE FINITE DOMAIN

- Mathematics, Computer Science
- The Bulletin of Symbolic Logic
- 2017

The aim of this article is to connect syntactic complexity, by which the authors mean the complexity of sentences and strengths of the theories in which they are provable, with the semantic concept of complexity of the computational problems represented by these sentences. Expand

On provably disjoint NP-pairs

- Computer Science, Mathematics
- Electron. Colloquium Comput. Complex.
- 1994

This paper study the pairs (U,V) of disjoint NP-sets representable in a theory T of Bounded Arithmetic in the sense that T proves U intersection V = \emptyset, which allows the approach to showing independence of central open questions in Boolean complexity from theories of Bounding Arithmetic to be clarified. Expand

New relations and separations of conjectures about incompleteness in the finite domain

- Mathematics, Computer Science
- ArXiv
- 2019

It is proved that existence of a p-optimal proof system for $\mathsf{TAUT}$ and existence ofA complete problem for $\ mathsf{TFNP}$ are independent of each other in relativized worlds which was not known before. Expand

Complexity Classes without Machines: On Complete Languages for UP

- Computer Science, Mathematics
- Theor. Comput. Sci.
- 1988

Techniques for studying complexity classes that are not covered by known recursive enumerations of machines are developed by using them to examine the probabilistic class BPP and it is shown that there is a relativized world where BPPA has no complete languages. Expand

Disjoint NP-Pairs

- Computer Science, Mathematics
- SIAM J. Comput.
- 2004

It is shown under reasonable hypotheses that nonsymmetric disjoint NP-pairs exist, which provides additional evidence for the existence of P-inseparable disj joint NP-Pairs. Expand

Nondeterministic functions and the existence of optimal proof systems

- Computer Science, Mathematics
- Theor. Comput. Sci.
- 2009

It is shown how different interpolation properties can be modeled by NP-pairs associated with the underlying proof system by characterize this problem by the question of whether every propositional proof system has the effective interpolation property. Expand

The Relative Efficiency of Propositional Proof Systems

- Computer Science
- J. Symb. Log.
- 1979

All standard Hilbert type systems and natural deduction systems are equivalent, up to application of a polynomial, as far as minimum proof length goes, and extended Frege systems are introduced, which allow introduction of abbreviations for formulas. Expand

Is the Standard Proof System for SAT P-Optimal?

- Mathematics, Computer Science
- FSTTCS
- 2000

This work investigates the question whether there is a (p-)optimal proof system for SAT or for TAUT and its relation to completeness and collapse results for nondeterministic function classes, and shows some relations between various completeness assumptions. Expand

Optimal proof systems imply complete sets for promise classes

- Computer Science, Mathematics
- Inf. Comput.
- 2003

The existence of (p-)optimal proof systems and the existence of complete problems for certain promise complexity classes like UP, NP ∩ Sparse, RP or BPP are shown. Expand