Related papers: Satisfiability of Non-Linear Transcendental Arithm…
In a seminal paper from 1985, Sistla and Clarke showed that satisfiability for Linear Temporal Logic (LTL) is either NP-complete or PSPACE-complete, depending on the set of temporal operators used. If, in contrast, the set of propositional…
The following paper proposes a new approach to determine whether a logical (CNF) formula is satisfiable or not using probability theory methods. Furthermore, we will introduce an algorithm that speeds up the standard solution for (CNF-SAT)…
Reasoning about array data structures is a key requirement for many applications in hardware and software verification, especially in combination with machine integers. The Satisfiability Modulo Theories (SMT) theory of extensional arrays…
Horn-satisfiability or Horn-SAT is the problem of deciding whether a satisfying assignment exists for a Horn formula, a conjunction of clauses each with at most one positive literal (also known as Horn clauses). It is a well-known…
Satisfiability Modulo the Theory of Nonlinear Real Arithmetic, SMT(NRA) for short, concerns the satisfiability of polynomial formulas, which are quantifier-free Boolean combinations of polynomial equations and inequalities with integer…
We determine the exact threshold of satisfiability for random instances of a particular NP-complete constraint satisfaction problem (CSP). This is the first random CSP model for which we have determined a precise linear satisfiability…
We show that time complexity analysis of higher-order functional programs can be effectively reduced to an arguably simpler (although computationally equivalent) verification problem, namely checking first-order inequalities for validity.…
In this paper we deal with verification of safety properties of term-rewriting systems. The verification problem is translated to a purely logical problem of finding a finite countermodel for a first-order formula, which further resolved by…
Linear Temporal Logic (LTL) is a widely used task specification language for autonomous systems. To mitigate the significant manual effort and expertise required to define LTL-encoded tasks, several methods have been proposed for…
The logical connectives typically found in programming languages are similar to their mathematical counterparts, yet different due to their short-circuit behaviour -- when evaluating them, the second argument is only evaluated if the first…
In the certification problem, the algorithm is given a function $f$ with certificate complexity $k$ and an input $x^\star$, and the goal is to find a certificate of size $\le \text{poly}(k)$ for $f$'s value at $x^\star$. This problem is in…
For formulas F of propositional calculus I introduce a "metavariable" MF and show how it can be used to define an algorithm for testing satisfiability. MF is a formula which is true/false under all possible truth assignments iff F is…
Boolean Satisfiability (SAT) problems are expressed as mathematical formulas. This paper presents a matrix representation for these SAT problems. It shows how to use this matrix representation to get the full set of valid satisfying…
We study the satisfiability problem for a modal logic expressing knowing-how assertions, which captures an agent's ability to achieve a given goal under the standard semantics based on linear plans. Our main result shows that satisfiability…
We study the problem of {\sl certification}: given queries to a function $f : \{0,1\}^n \to \{0,1\}$ with certificate complexity $\le k$ and an input $x^\star$, output a size-$k$ certificate for $f$'s value on $x^\star$. This abstractly…
In many decision-making processes, one may prefer multiple solutions to a single solution, which allows us to choose an appropriate solution from the set of promising solutions that are found by algorithms. Given this, finding a set of…
A reliable method for characterizing quantum operations that is suitable for improving and validating their accuracies is indispensable for realizing a practical quantum computer. Known methods are still not sufficient because they lack…
While reachability analysis is one of the most promising approaches for formal verification of dynamic systems, a major disadvantage preventing a more widespread application is the requirement to manually tune algorithm parameters such as…
Satisfiability Modulo Theories (SMT) refers to the problem of deciding the satisfiability of a formula with respect to certain background first order theories. In this paper, we focus on Satisfiablity Modulo Integer Arithmetic, which is…
An important aspect in the solution process of constraint satisfaction problems is to identify exclusion boxes which are boxes that do not contain feasible points. This paper presents a certificate of infeasibility for finding such boxes by…