相关论文: The Complexity of Boolean Constraint Isomorphism

We give a complexity dichotomy theorem for the counting Constraint Satisfaction Problem (#CSP in short) with complex weights. To this end, we give three conditions for its tractability. Let F be any finite set of complex-valued functions,…

We intend to create new concepts aimed at finding necessary and sufficient conditions for Boolean satisfiability so that these conditions can be verified in polynomial time. Based on these conditions it will be possible to create an…

The Kochen-Specker no-go theorem established that hidden-variable theories in quantum mechanics necessarily admit contextuality. This theorem is formally stated in terms of the partial Boolean algebra structure of projectors on a Hilbert…

We prove the #P-hardness of the counting problems associated with various satisfiability, graph and combinatorial problems, when restricted to planar instances. These problems include \begin{romannum} \item[{}] {\sc 3Sat, 1-3Sat, 1-Ex3Sat,…

Deciding whether a graph can be embedded in a grid using only unit-length edges is NP-complete, even when restricted to binary trees. However, it is not difficult to devise a number of graph classes for which the problem is polynomial, even…

Given a pair of graphs $\textbf{A}$ and $\textbf{B}$, the problems of deciding whether there exists either a homomorphism or an isomorphism from $\textbf{A}$ to $\textbf{B}$ have received a lot of attention. While graph homomorphism is…

Many complex questions in biology, physics, and mathematics can be mapped to the graph isomorphism problem and the closely related graph automorphism problem. In particular, these problems appear in the context of network visualization,…

While 3-SAT is NP-hard, 2-SAT is solvable in polynomial time. Austrin, Guruswami, and H\r{a}stad roved a result known as "$(2+\varepsilon)$-SAT is NP-hard" [FOCS'14/SICOMP'17]. They showed that the problem of distinguishing k-CNF formulas…

Constraint satisfaction problems (or CSPs) have been extensively studied in, for instance, artificial intelligence, database theory, graph theory, and statistical physics. From a practical viewpoint, it is beneficial to approximately solve…

Satisfiability problems play a central role in computer science and engineering as a general framework for studying the complexity of various problems. Schaefer proved in 1978 that truth satisfaction of propositional formulas given a…

We consider the complexity of counting homomorphisms from an $r$-uniform hypergraph $G$ to a symmetric $r$-ary relation $H$. We give a dichotomy theorem for $r>2$, showing for which $H$ this problem is in FP and for which $H$ it is…

The Dichotomy Conjecture for constraint satisfaction problems (CSPs) states that every CSP is in P or is NP-complete (Feder-Vardi, 1993). It has been verified for conservative problems (also known as list homomorphism problems) by A.…

Hybrid logic with binders is an expressive specification language. Its satisfiability problem is undecidable in general. If frames are restricted to N or general linear orders, then satisfiability is known to be decidable, but of…

We prove a complexity dichotomy theorem for a class of Holant problems on planar 3-regular bipartite graphs. The complexity dichotomy states that for every weighted constraint function $f$ defining the problem (the weights can even be…

We determine the computational complexity of approximately counting the total weight of variable assignments for every complex-weighted Boolean constraint satisfaction problem (or CSP) with any number of additional unary (i.e., arity 1)…

Boolean satisfiability problem has applications in various fields. An efficient algorithm to solve satisfiability problem can be used to solve many other problems efficiently. The input of satisfiability problem is a finite set of clauses.…

Correspondence homomorphisms are both a generalization of standard homomorphisms and a generalization of correspondence colourings. For a fixed target graph $H$, the problem is to decide whether an input graph $G$, with each edge labeled by…

In this paper, I consider a fine-grained dichotomy of Boolean counting constraint satisfaction problem (#CSP), under the exponential time hypothesis of counting version (#ETH). Suppose $\mathscr{F}$ is a finite set of algebraic…

We show NP-completeness for several planar variants of the monotone satisfiability problem with bounded variable appearances. With one exception the presented variants have an associated bipartite graph where the vertex degree is bounded by…

Representing graphs by their homomorphism counts has led to the beautiful theory of homomorphism indistinguishability in recent years. Moreover, homomorphism counts have promising applications in database theory and machine learning, where…