On the complement of one complexity class in another

1984 ◽  
pp. 77-87 ◽  
Author(s):  
Diana Schmidt
Keyword(s):  
Complexity Class

Logical Characterizations of Bounded Query Classes I: Logspace Oracle Machines

1993 ◽  
Vol 18 (1) ◽  
pp. 65-92
Author(s):  
Iain A. Stewart
Keyword(s):  
Truth Table ◽  
Complexity Class ◽  
Polynomial Hierarchy ◽  
Complexity Classes ◽  
Turing Machines ◽  
Complete Problems

We consider three sub-logics of the logic (±HP)*[FOs] and show that these sub-logics capture the complexity classes obtained by considering logspace deterministic oracle Turing machines with oracles in NP where the number of oracle calls is unrestricted and constant, respectively; that is, the classes LNP and LNP[O(1)]. We conclude that if certain logics are of the same expressibility then the Polynomial Hierarchy collapses. We also exhibit some new complete problems for the complexity class LNP via projection translations (the first to be discovered: projection translations are extremely weak logical reductions between problems) and characterize the complexity class LNP[O(1)] as the closure of NP under a new, extremely strict truth-table reduction (which we introduce in this paper).

Strong extension axioms and Shelah's zero-one law for choiceless polynomial time

2003 ◽  
Vol 68 (1) ◽  
pp. 65-131 ◽  
Author(s):  
Andreas Blass ◽  
Yuri Gurevich
Keyword(s):  
Fixed Point ◽  
Polynomial Time ◽  
Order Logic ◽  
Complexity Class ◽  
First Order Logic ◽  
Infinitary Logic ◽  
Extensive Discussion ◽  
First Order ◽  
Detailed Proof ◽  
Strong Extension

AbstractThis paper developed from Shelah's proof of a zero-one law for the complexity class “choiceless polynomial time,” defined by Shelah and the authors. We present a detailed proof of Shelah's result for graphs, and describe the extent of its generalizability to other sorts of structures. The extension axioms, which form the basis for earlier zero-one laws (for first-order logic, fixed-point logic, and finite-variable infinitary logic) are inadequate in the case of choiceless polynomial time; they must be replaced by what we call the strong extension axioms. We present an extensive discussion of these axioms and their role both in the zero-one law and in general.

scholarly journals Combinatorial Nullstellensatz Modulo Prime Powers and the Parity Argument

10.37236/4124 ◽  
2014 ◽  
Vol 21 (4) ◽  
Author(s):  
László Varga
Keyword(s):  
Complexity Class ◽  
Combinatorial Nullstellensatz ◽  
Search Problem ◽  
Search Problems ◽  
Computational Search

We present new generalizations of Olson's theorem and of a consequence of Alon's Combinatorial Nullstellensatz. These enable us to extend some of their combinatorial applications with conditions modulo primes to conditions modulo prime powers. We analyze computational search problems corresponding to these kinds of combinatorial questions and we prove that the problem of finding degree-constrained subgraphs modulo $2^d$ such as $2^d$-divisible subgraphs and the search problem corresponding to the Combinatorial Nullstellensatz over $\mathbb{F}_2$ belong to the complexity class Polynomial Parity Argument (PPA).

scholarly journals Characterizations of periods of multi-dimensional shifts

2013 ◽  
Vol 35 (2) ◽  
pp. 431-460 ◽  
Author(s):  
EMMANUEL JEANDEL ◽  
PASCAL VANIER
Keyword(s):  
Finite Type ◽  
Complexity Class ◽  
Space Complexity

AbstractWe show that the sets of periods of multi-dimensional shifts of finite type are precisely the sets of integers of the complexity classNP. We also show that the functions counting their number are the functions of #P. We also give characterizations of some other notions of periodicity in terms of space complexity. We finish the paper by giving some characterizations for sofic and effective subshifts.

ON CENTRALIZED PARALLEL COMMUNICATING GRAMMAR SYSTEMS WITH CONTEXT-SENSITIVE COMPONENTS

2013 ◽  
Vol 24 (04) ◽  
pp. 453-471
Author(s):  
FRIEDRICH OTTO
Keyword(s):  
Time Complexity ◽  
Complexity Class ◽  
Context Sensitive ◽  
Grammar Systems ◽  
Parallel Communicating Grammar Systems

Centralized parallel communicating grammar systems with context-sensitive components that work in returning mode can only generate context-sensitive languages. Here we show that, when working in nonreturning mode, these grammar systems generate all languages from the nondeterministic time complexity class NEXT = ∪c ≥ 1 NTIME (2c·n).

scholarly journals Dyn-FO: A Parallel, Dynamic Complexity Class

1997 ◽  
Vol 55 (2) ◽  
pp. 199-209 ◽  
Author(s):  
Sushant Patnaik ◽  
Neil Immerman
Keyword(s):  
Complexity Class ◽  
Dynamic Complexity

scholarly journals Design and implementation of aggregate functions in the DLV system

2008 ◽  
Vol 8 (5-6) ◽  
pp. 545-580 ◽  
Author(s):  
WOLFGANG FABER ◽  
GERALD PFEIFER ◽  
NICOLA LEONE ◽  
TINA DELL'ARMI ◽  
GIUSEPPE IELPA
Keyword(s):  
Computational Complexity ◽  
Logic Programming ◽  
Real World ◽  
State Of The Art ◽  
Complexity Class ◽  
Natural Manner ◽  
Design And Implementation ◽  
Finite Structures ◽  
Real World Applications ◽  
Aggregate Functions

AbstractDisjunctive logic programming (DLP) is a very expressive formalism. It allows for expressing every property of finite structures that is decidable in the complexity class ΣP2(=NPNP). Despite this high expressiveness, there are some simple properties, often arising in real-world applications, which cannot be encoded in a simple and natural manner. Especially properties that require the use of arithmetic operators (like sum, times, or count) on a set or multiset of elements, which satisfy some conditions, cannot be naturally expressed in classic DLP. To overcome this deficiency, we extend DLP by aggregate functions in a conservative way. In particular, we avoid the introduction of constructs with disputed semantics, by requiring aggregates to be stratified. We formally define the semantics of the extended language (called ), and illustrate how it can be profitably used for representing knowledge. Furthermore, we analyze the computational complexity of , showing that the addition of aggregates does not bring a higher cost in that respect. Finally, we provide an implementation of in DLV—a state-of-the-art DLP system—and report on experiments which confirm the usefulness of the proposed extension also for the efficiency of computation.

scholarly journals Sparse complete sets for coNP: Solution of the P versus NP problem

2021 ◽  
Author(s):  
Frank Vega
Keyword(s):  
Computer Science ◽  
Fundamental Question ◽  
Complexity Class ◽  
Open Problems ◽  
Precise Statement ◽  
Complete Sets ◽  
Np Problem

P versus NP is considered as one of the most important open problems in computer science. This consists in knowing the answer of the following question: Is P equal to NP? A precise statement of the P versus NP problem was introduced independently by Stephen Cook and Leonid Levin. Since that date, all efforts to find a proof for this problem have failed. Another major complexity class is coNP. Whether NP = coNP is another fundamental question that it is as important as it is unresolved. In 1979, Fortune showed that if any sparse language is coNP-complete, then P = NP. We prove there is a possible sparse language in coNP-complete. In this way, we demonstrate the complexity class P is equal to NP.

scholarly journals Robustness of QMA against witness noise

2017 ◽  
Vol 17 (13&14) ◽  
pp. 1167-1190
Author(s):  
Friederike Anna Dziemba
Keyword(s):  
Complexity Class ◽  
Complexity Classes ◽  
Unified Framework ◽  
The Relationship

Using the tool of concatenated stabilizer coding, we prove that the complexity class QMA remains unchanged even if every witness qubit is disturbed by constant noise. This result may not only be relevant for physical implementations of verifying protocols but also attacking the relationship between the complexity classes QMA, QCMA and BQP, which can be reformulated in this unified framework of a verifying protocol receiving a disturbed witness. While QCMA and BQP are described by fully dephasing and depolarizing channels on the witness qubits, respectively, our result proves QMA to be robust against 27% dephasing and 18% depolarizing noise.

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