Related papers: Transformer Encoder Satisfiability: Complexity and…
We study succinctness as a measure of the expressive power of transformers. Succinctness -- how compactly a formalism can describe a language relative to other formalisms -- is a classical notion in logic and automata theory. We prove that…
We investigate the satisfiability and finite satisfiability problem for probabilistic computation-tree logic (PCTL) where operators are not restricted by any step bounds. We establish decidability for several fragments containing…
The study of word equations (or the existential theory of equations over free monoids) is a central topic in mathematics and theoretical computer science. The problem of deciding whether a given word equation has a solution was shown to be…
We study finite first-order satisfiability (FSAT) in the constructive setting of dependent type theory. Employing synthetic accounts of enumerability and decidability, we give a full classification of FSAT depending on the first-order…
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…
The satisfiability problem for SPARQL patterns is undecidable in general, since the expressive power of SPARQL 1.0 is comparable with that of the relational algebra. The goal of this paper is to delineate the boundary of decidability of…
We investigate the properties of formal languages expressible in terms of formulas over quantifier-free theories of word equations, arithmetic over length constraints, and language membership predicates for the classes of regular, visibly…
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…
Mechanistic interpretability often identifies circuits inside Transformer models, but explanations of those circuits are usually validated through examples, ablations, and manual reasoning. This leaves a gap between finding a plausible…
In this paper we investigate formal verification problems for Neural Network computations. Various reachability problems will be in the focus, such as: Given symbolic specifications of allowed inputs and outputs in form of Linear…
This paper shows effectiveness of X3SAT in proving P = NP. This is due to the fact that it is easy to check unsatisfiability of a particular truth assignment. A truth assignment leads to some reductions of clauses by means of "exactly-1…
Fundamentally, every static program analyser searches for a proof through a combination of heuristics providing candidate solutions and a candidate validation technique. Essentially, the heuristic reduces a second-order problem to a…
We study the satisfiability of string constraints where context-free membership constraints may be imposed on variables. Additionally a variable may be constrained to be a subword of a word obtained by shuffling variables and their…
Parity reasoning is challenging for Conflict-Driven Clause Learning (CDCL) SAT solvers. This has been observed even for simple formulas encoding two contradictory parity constraints with different variable orders (Chew and Heule 2020). We…
We propose a fragment of many-sorted second order logic called EQSMT and show that checking satisfiability of sentences in this fragment is decidable. EQSMT formulae have an $\exists^*\forall^*$ quantifier prefix (over variables, functions…
The synthesis problem asks to automatically generate, if it exists, an algorithm from a specification of correct input-output pairs. In this paper, we consider the synthesis of computable functions of infinite words, for a classical Turing…
The decidability of equivalence for three important classes of tree transducers is discussed. Each class can be obtained as a natural restriction of deterministic macro tree transducers (MTTs): (1) no context parameters, i.e., top-down tree…
Boolean Satisfiability Problem (SAT) is one of the core problems in computer science. As one of the fundamental NP-complete problems, it can be used - by known reductions - to represent instances of variety of hard decision problems.…
We consider the weighted antimonotone and the weighted monotone satisfiability problems on normalized circuits of depth at most $t \geq 2$, abbreviated {\sc wsat$^-[t]$} and {\sc wsat$^+[t]$}, respectively. These problems model the weighted…
The verification of systems combining hard timing constraints with concurrency is challenging. This challenge becomes even harder when some timing constants are missing or unknown. Parametric timed formalisms, such as parametric timed…