Related papers: The Computational Complexity of Satisfiability in …
We study computable topological spaces and semicomputable and computable sets in these spaces. In particular, we investigate conditions under which semicomputable sets are computable. We prove that a semicomputable compact manifold $M$ is…
The constraint satisfaction problem asks to decide if a set of constraints over a relational structure $\mathcal{A}$ is satisfiable (CSP$(\mathcal{A})$). We consider CSP$(\mathcal{A} \cup \mathcal{B})$ where $\mathcal{A}$ is a structure and…
Here we study the NP-complete $K$-SAT problem. Although the worst-case complexity of NP-complete problems is conjectured to be exponential, there exist parametrized random ensembles of problems where solutions can typically be found in…
We study the connection between the order of phase transitions in combinatorial problems and the complexity of decision algorithms for such problems. We rigorously show that, for a class of random constraint satisfaction problems, a limited…
We systematically investigate the complexity of model checking the existential positive fragment of first-order logic. In particular, for a set of existential positive sentences, we consider model checking where the sentence is restricted…
Weighted knowledge bases for description logics with typicality under a "concept-wise" multi-preferential semantics provide a logical interpretation of MultiLayer Perceptrons. In this context, Answer Set Programming (ASP) has been shown to…
We determine the complexity of several constraint satisfaction problems using the heuristic algorithm, WalkSAT. At large sizes N, the complexity increases exponentially with N in all cases. Perhaps surprisingly, out of all the models…
Random constraint satisfaction problems (CSPs) such as random $3$-SAT are conjectured to be computationally intractable. The average case hardness of random $3$-SAT and other CSPs has broad and far-reaching implications on problems in…
The systematic modelling of dynamic spatial systems is a key requirement in a wide range of application areas such as commonsense cognitive robotics, computer-aided architecture design, and dynamic geographic information systems. We present…
We develop a simple functional programming language aimed at manipulating infinite, but first-order definable structures, such as the countably infinite clique graph or the set of all intervals with rational endpoints. Internally, such sets…
Modal logic S5 has attracted significant attention and has led to several practical applications, owing to its simplified approach to dealing with nesting modal operators. Efficient implementations for evaluating satisfiability of S5…
There is a subset of computational problems that are computable in polynomial time for which an existing algorithm may not complete due to a lack of high performance technology on a mission field. We define a subclass of deterministic…
Sign-Perturbed Sum (SPS) is a powerful finite-sample system identification algorithm which can construct confidence regions for the true data generating system with exact coverage probabilities, for any finite sample size. SPS was developed…
In recent years there has been considerable interest in theories over string equations, length function, and string-number conversion predicate within the formal verification, software engineering, and security communities. SMT solvers for…
In this paper, we address complexity issues for timeline-based planning over dense temporal domains. The planning problem is modeled by means of a set of independent, but interacting, components, each one represented by a number of state…
State space models (SSMs) have gained attention by showing potential to outperform Transformers. However, previous studies have not sufficiently addressed the mechanisms underlying their high performance owing to a lack of theoretical…
Constraint Satisfaction Problem on finite sets is known to be NP-complete in general but certain restrictions on the constraint language can ensure tractability. It was proved that if a constraint language has a weak near unanimity…
A semi-computable set S in a computable metric space need not be computable. However, in some cases, if S has certain topological properties, we can conclude that S is computable. It is known that if a semi-computable set S is a compact…
We study the complexity of Boolean constraint satisfaction problems (CSPs) when the assignment must have Hamming weight in some congruence class modulo M, for various choices of the modulus M. Due to the known classification of tractable…
This paper addresses the quantitative verification of finite-time constrained occupation time for stochastic continuous-time systems governed by stochastic differential equations (SDEs). Unlike classical reachability analysis, which focuses…