Dichotomy theorem
In computational complexity theory, a branch of computer science, Schaefer's dichotomy theorem states necessary and sufficient conditions under which a finite set S of relations over the Boolean domain yields polynomial-time or NP-complete problems when the relations of S are used to … See more Schaefer defines a decision problem that he calls the Generalized Satisfiability problem for S (denoted by SAT(S)), where $${\displaystyle S=\{R_{1},\ldots ,R_{m}\}}$$ is a finite set of relations over propositional … See more The analysis was later fine-tuned: CSP(Γ) is either solvable in co-NLOGTIME, L-complete, NL-complete, ⊕L-complete, P-complete or NP-complete and given Γ, one can decide in … See more • Max/min CSP/Ones classification theorems, a similar set of constraints for optimization problems See more A modern, streamlined presentation of Schaefer's theorem is given in an expository paper by Hubie Chen. In modern terms, the problem SAT(S) is viewed as a See more Given a set Γ of relations, there is a surprisingly close connection between its polymorphisms and the computational complexity of CSP(Γ). A relation R is … See more If the problem is to count the number of solutions, which is denoted by #CSP(Γ), then a similar result by Creignou and Hermann holds. Let Γ be a finite constraint language over the Boolean domain. The problem #CSP(Γ) is computable in polynomial time if Γ … See more WebApr 2, 2015 · The main result of the paper states that a minimal system is either multi-sensitive or an almost one-to-one extension of its maximal equicontinuous factor, which …
Dichotomy theorem
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WebSep 27, 2013 · Under a strong twist condition, we prove the following dichotomy: they are either Birkhoff, and thus very regular, or extremely irregular and non-physical: they then grow exponentially and oscillate. For Birkhoff minimizers, we also prove certain strong ordering properties that are well known for twist maps. WebDichotomy Theorems Arise Theorem (Goldberg, Grohe, Jerrum and Thurley 09) Given any symmetric matrix A 2R A m m, Eval(A) is either solvable in P-time or #P-hard. Theorem (Cai, C and Lu 11) Given any symmetric matrix A 2C A m m, Eval(A) is either solvable in P-time or #P-hard.
WebMain Dichotomy Theorem Theorem (C, Chen and Lu) There is a complexity dichotomy theorem for EVAL(A). For any symmetric complex vlaued matrix A ∈ Cm×m, the problem of computing Z A(G), for any input G, is either in P or #P-hard. 14 WebBy Grabrielov’s Theorem on the comple-ment and a Lojasiewicz result on connected components of se! mianalytic sets (see [BM],[L],[LZ]) R an is o-minimal. Example 1.6. Let R exp =(R,+,·,exp). Wilkie [W1]provedthatR exp is model complete, as a direct consequence of this theorem each definable sets in R exp is the image of the zero set of a ...
WebApr 22, 2024 · The complexity of graph homomorphism problems has been the subject of intense study for some years. In this paper, we prove a decidable complexity dichotomy theorem for the partition function of directed graph homomorphisms. Our theorem applies to all non-negative weighted forms of the problem: given any fixed matrix A with non … Webcomplexity dichotomy theorems. Such theoremsstate thateverymemberoftheclassofproblemsconcernediseithertractable(i.e.,solvable …
WebOur main theorem is that under the Ultrapower Axiom, a countably complete ultrafilter has at most finitely many predecessors in the Rudin-Frolík order. In other words, any wellfounded ultrapower (of the universe) is the ultrapower of at most finitely many ultrapowers. ... a proof of Woodin's HOD dichotomy theorem from a single strongly …
WebDichotomy Theorems for Counting Creignou and Hermann proved a dichotomy theorem for counting SAT problems: Either solvable in P or #P-complete. Creignou, Khanna and … fluids conservation of energyWebA NOTE ON GOWERS’ DICHOTOMY THEOREM 151 non zero vectors in a normed space X is called C-unconditional if X "iaiei ° • C X aiei for any sequence of signs "i = §1 and … green eyes in the worldWebLater the Auslander-Yorke dichotomy theorem was refined in [3], [17]: a transitive system is either sensitive or almost equicontinuous (in the sense of containing some … greeneyes manufacturingWebSeparation dichotomy and wavefronts for a nonlinear convolution equation fluids coming out of noseWebMar 12, 2014 · The equivalences alluded to above follow from our main theorem and the results of [3]. That monograph had previously shown that (I) and (II) are incompatible, and proved a barbaric forerunner of 1.1, and gone on to conjecture the dichotomy result above. green eyes in newborn babyWebvalues belongs to the underlying relation. Schaefer’s main result is a dichotomy theorem for the computational complexity of SAT(A), namely, depending on A, either SAT(A) is NP-complete or SAT(A) is solvable in polynomial time. Schaefer’s dichotomy theorem provided a unifying explanation for the NP-completeness of many well-known variants of fluids conservation of mass equationWebIn particular, many Silver-style dichotomy theorems can be obtained from the Kechris-Solecki-Todorcevic characterization of the class of an-alytic graphs with countable Borel chromatic number [11]. In x2, we give a classical proof that ideals arising from a natural spe-cial case of the Kechris-Solecki-Todorcevic dichotomy theorem [11] have green eyes llc easton md