Related papers: Transformer Encoder Satisfiability: Complexity and…
We study the satisfiability problem of symbolic tree automata and decompose it into the satisfiability problem of the existential first-order theory of the input characters and the existential monadic second-order theory of the indices of…
Previous work has shown that reasoning with real-time temporal logics is often simpler when restricted to models with bounded variability---where no more than v events may occur every V time units, for given v, V. When reasoning about…
It is well-know that deciding consistency for normal answer set programs (ASP) is NP-complete, thus, as hard as the satisfaction problem for classical propositional logic (SAT). The best algorithms to solve these problems take exponential…
The Circuit Satisfiability (CSAT) problem, a variant of the Boolean Satisfiability (SAT) problem, plays a critical role in integrated circuit design and verification. However, existing SAT solvers, optimized for Conjunctive Normal Form…
Ising machines are emerging as a new technology for solving various classes of computationally hard problems of practical importance, yet their limits on structured SAT workloads, representative of numerous real-world applications, remain…
Recent theoretical results show transformers cannot express sequential reasoning problems over long inputs, intuitively because their computational depth is bounded. However, prior work treats the depth as a constant, leaving it unclear to…
Obstacles to integrability sometimes hamper the standard Normal Form analysis of perturbed integrable evolution equations. One is then forced to account for them by the Normal Form, which is the dynamical equation obeyed by the zero-order…
We study formal languages which are capable of fully expressing quantitative probabilistic reasoning and do-calculus reasoning for causal effects, from a computational complexity perspective. We focus on satisfiability problems whose…
The constraint satisfaction probem (CSP) is a well-acknowledged framework in which many combinatorial search problems can be naturally formulated. The CSP may be viewed as the problem of deciding the truth of a logical sentence consisting…
We investigate regular realizability (RR) problems, which are the problems of verifying whether intersection of a regular language -- the input of the problem -- and fixed language called filter is non-empty. We consider two kind of…
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…
Patterns are words with terminals and variables. The language of a pattern is the set of words obtained by uniformly substituting all variables with words that contain only terminals. Length constraints restrict valid substitutions of…
In this paper, we consider the satisfiability problem for string logic with equations, regular membership and Presburger constraints over length functions. The difficulty comes from multiple occurrences of string variables making…
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…
Automatic synthesis from linear temporal logic (LTL) specifications is widely used in robotic motion planning, control of autonomous systems, and load distribution in power networks. A common specification pattern in such applications…
Compositions of tree-walking tree transducers form a hierarchy with respect to the number of transducers in the composition. As main technical result it is proved that any such composition can be realized as a linear bounded composition,…
We study elementary modal logics, i.e. modal logic considered over first-order definable classes of frames. The classical semantics of modal logic allows infinite structures, but often practical applications require to restrict our…
Patterns are words with terminals and variables. The language of a pattern is the set of words obtained by uniformly substituting all variables with words that contain only terminals. Regular constraints restrict valid substitutions of…
We study various novel complexity measures for two-sided matching mechanisms, applied to the two canonical strategyproof matching mechanisms, Deferred Acceptance (DA) and Top Trading Cycles (TTC). Our metrics are designed to capture the…
Random instances of constraint satisfaction problems such as k-SAT provide challenging benchmarks. If there are m constraints over n variables there is typically a large range of densities r=m/n where solutions are known to exist with…