Related papers: A New Structural Property of SAT
This paper gives a novel approach to analyze SAT problem more deeply. First, I define new elements of Boolean formula such as dominant variable, decision chain, and chain coupler. Through the analysis of the SAT problem using the elements,…
An ordinal view of independence is studied in the framework of possibility theory. We investigate three possible definitions of dependence, of increasing strength. One of them is the counterpart to the multiplication law in probability…
The boolean satisfiability (SAT) problem asks whether there exists an assignment of boolean values to the variables of an arbitrary boolean formula making the formula evaluate to True. It is well-known that all NP-problems can be coded as…
The amount of information in satisfiability problem (SAT) is considered. SAT can be polynomial-time solvable when the solving algorithm holds an exponential amount of information. It is also established that SAT Kolmogorov complexity is…
In this article, we show that the completion problem, i.e. the decision problem whether a partial structure can be completed to a full structure, is NP-complete for many combinatorial structures. While the gadgets for most reductions in…
In this paper, by constructing extremely hard examples of CSP (with large domains) and SAT (with long clauses), we prove that such examples cannot be solved without exhaustive search, which is stronger than P $\neq$ NP. This constructive…
Structural independence is the (conditional) independence that arises from the structure rather than the precise numerical values of a distribution. We develop this concept and relate it to $d$-separation and structural causal models.…
A strong backdoor in a formula $\phi$ of propositional logic to a tractable class $\mathcal{C}$ of formulas is a set $B$ of variables of $\phi$ such that every assignment of the variables in $B$ results in a formula from $\mathcal{C}$.…
In this paper, we investigate the hitting set problem and demonstrate that solution independence is the crucial property underlying the construction of self-referential instances. As a special case of the hitting set problem, the vertex…
The Boolean satisfiability problem (SAT) holds a central place in computational complexity theory as the first shown NP-complete problem. Due to this role, SAT is often used as the benchmark for polynomial-time reductions: if a problem can…
This paper presents a novel SAT-based approach for the computation of extensions in abstract argumentation, with focus on preferred semantics, and an empirical evaluation of its performances. The approach is based on the idea of reducing…
The classical satisfiability problem (SAT) is used as a natural and general tool to express and solve combinatorial problems that are in NP. We postulate that provability for implicational intuitionistic propositional logic (IIPC) can serve…
Propositional satisfiability (SAT) is one of the most fundamental problems in computer science. The worst-case hardness of SAT lies at the core of computational complexity theory. The average-case analysis of SAT has triggered the…
Interference is a phenomenon on proof systems for SAT solving that is both counter-intuitive and bothersome when developing proof-logging techniques. However, all existing proof systems that can produce short proofs for all inprocessing…
Recently, Xu and Zhou [2023] introduced a constructive approach for exploring computational hardness, proving that SAT requires exhaustive search. In light of certain misinterpretations concerning the contributions and proofs in that paper,…
We develop a new notion of independence suggested by Scanlon (th-independence). We prove that in a large class of theories (which includes all simple theories) this notion has many of the properties needed for an adequate geometric…
In this paper the reason why entropy reduction (negentropy) can be used to measure the complexity of any computation was first elaborated both in the aspect of mathematics and informational physics. In the same time the equivalence of…
On the one hand, Constraint Satisfaction Problems allow one to declaratively model problems. On the other hand, propositional satisfiability problem (SAT) solvers can handle huge SAT instances. We thus present a technique to declaratively…
Independence of premise principles play an important role in characterizing the modified realizability and the Dialectica interpretations. In this paper we show that a great many intuitionistic set theories are closed under the…
We study constrained versions of the Ingleton inequality in the entropic setting and quantify its stability under small violations of conditional independence. Although the classical Ingleton inequality fails for general entropy profiles,…