Related papers: Boolean Satisfiability with Transitivity Constrain…
Decision procedures can be either theory-specific, e.g., Presburger arithmetic, or theory-generic, applying to an infinite number of user-definable theories. Variant satisfiability is a theory-generic procedure for quantifier-free…
Optimization problems such as the NP-complete 3-SAT provide an important benchmark for the difficult task of finding ground-states in strongly correlated many-body systems with rugged energy landscapes. The study of random 3-SAT problems as…
We generalize many results concerning the tractability of SAT and #SAT on bounded treewidth CNF-formula in the context of Quantified Boolean Formulas (QBF). To this end, we start by studying the notion of width for OBDD and observe that the…
For arbitrary undirected graph $G$, we are designing SATISFIABILITY problem (SAT) for HCP, using tools of Boolean algebra only. The obtained SAT be the logic formulation of conditions for Hamiltonian cycle existence, and use $m$ Boolean…
In this paper, we address the problem of the (reactive) realizability of specifications of theories richer than Booleans, including arithmetic theories. Our approach transforms theory specifications into purely Boolean specifications by (1)…
Two major considerations when encoding pseudo-Boolean (PB) constraints into SAT are the size of the encoding and its propagation strength, that is, the guarantee that it has a good behaviour under unit propagation. Several encodings with…
Certifying feasibility in decision-making, critical in many industries, can be framed as a constraint satisfaction problem. This paper focuses on characterising a subset of parameter values from an a priori set that satisfy constraints on a…
We present a formulation of the Boolean Satisfiability Problem in spinor language that allows to give a necessary and sufficient condition for unsatisfiability. With this result we outline an algorithm to test for unsatisfiability with…
We compare three satisfiability notions for propositional formulas in the language {not, and, or} over a fixed finite-dimensional Hilbert space H=F^d with F in {R, C}. The first is the standard Hilbert-lattice semantics on the subspace…
The problem of estimating the proportion of satisfiable instances of a given CSP (constraint satisfaction problem) can be tackled through weighting. It consists in putting onto each solution a non-negative real value based on its…
Many reasoning problems are based on the problem of satisfiability (SAT). While SAT itself becomes easy when restricting the structure of the formulas in a certain way, the situation is more opaque for more involved decision problems. We…
The Exact Satisfiability problem asks if we can find a satisfying assignment to each clause such that exactly one literal in each clause is assigned $1$, while the rest are all assigned $0$. We can generalise this problem further by…
The reactive synthesis problem is to compute a system satisfying a given specification in temporal logic. Bounded synthesis is the approach to bound the maximum size of the system that we accept as a solution to the reactive synthesis…
Many software as well digital hardware automatic synthesis methods define the set of implementations meeting the given system specifications with a boolean relation K. In such a context a fundamental step in the software (hardware)…
All solutions SAT (AllSAT for short) is a variant of propositional satisfiability problem. Despite its significance, AllSAT has been relatively unexplored compared to other variants. We thus survey and discuss major techniques of AllSAT…
Understanding the characteristics of neural networks is important but difficult due to their complex structures and behaviors. Some previous work proposes to transform neural networks into equivalent Boolean expressions and apply…
For Boolean satisfiability problems, the structure of the solution space is characterized by the solution graph, where the vertices are the solutions, and two solutions are connected iff they differ in exactly one variable. For this…
We analyse the complexity of the satisfiability problem ssmSAT for State Space Models (SSM), which asks whether an input sequence can lead the model to an accepting configuration. We find that ssmSAT is undecidable in general, reflecting…
We consider entailment problems involving powerful constraint languages such as frontier-guarded existential rules in which we impose additional semantic restrictions on a set of distinguished relations. We consider restricting a relation…
Algorithmic meta-theorems state that problems definable in a fixed logic can be solved efficiently on structures with certain properties. An example is Courcelle's Theorem, which states that all problems expressible in monadic second-order…