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Program transformations are widely used in synthesis, optimization, and maintenance of software. Correctness of program transformations depends on preservation of some important properties of the input program. By regarding programs as…
Motivated by interpretability and reliability, we investigate whether large language models (LLMs) deploy universal geometric structures to encode discrete, graph-structured knowledge. To this end, we present two complementary experimental…
Finite linear least squares is one of the core problems of numerical linear algebra, with countless applications across science and engineering. Consequently, there is a rich and ongoing literature on algorithms for solving linear least…
The need to model and analyse dynamic systems operating over complex data is ubiquitous in AI and neighboring areas, in particular business process management. Analysing such data-aware systems is a notoriously difficult problem, as they…
Interval Temporal Logic (ITL) is an established temporal formalism for reasoning about time periods. For over 25 years, it has been applied in a number of ways and several ITL variants, axiom systems and tools have been investigated. We…
The language Timed Concurrent Constraint (tccp) is the extension over time of the Concurrent Constraint Programming (cc) paradigm that allows us to specify concurrent systems where timing is critical, for example reactive systems. Systems…
Quantified CTL (QCTL) is a well-studied temporal logic that extends CTL with quantification over atomic propositions. It has recently come to the fore as a powerful intermediary framework to study logics for strategic reasoning. We extend…
DatalogMTL extends the classical Datalog language with metric temporal logic (MTL), enabling expressive reasoning over temporal data. While existing reasoning approaches, such as materialisation based and automata based methods, offer…
DatalogMTL is an extension of Datalog with operators from metric temporal logic which has received significant attention in recent years. It is a highly expressive knowledge representation language that is well-suited for applications in…
We consider here Linear Temporal Logic (LTL) formulas interpreted over \emph{finite} traces. We denote this logic by LTLf. The existing approach for LTLf satisfiability checking is based on a reduction to standard LTL satisfiability…
Current evaluations of mathematical reasoning in large language models (LLMs) are dominated by static benchmarks, either derived from competition-style problems or curated through costly expert effort, resulting in limited coverage of…
Self-similar groups provide a rich source of groups with interesting properties; e.g., infinite torsion groups (Burnside groups) and groups with an intermediate word growth. Various self-similar groups can be described by a recursive…
Model counting is the problem of computing the number of models that satisfy a given propositional theory. It has recently been applied to solving inference tasks in probabilistic logic programming, where the goal is to compute the…
Modeling of physical systems includes extensive use of software packages that implement the accurate finite element method for solving differential equations considered along with the appropriate initial and boundary conditions. When the…
Model-checking HyperLTL, a temporal logic expressing properties of sets of traces with applications to information-flow based security and privacy, has a decidable, but TOWER-complete, model-checking problem. While the classical…
This work establishes a rigorous theoretical foundation for analyzing deep learning systems by leveraging Infinite Time Turing Machines (ITTMs), which extend classical computation into transfinite ordinal steps. Using ITTMs, we reinterpret…
Formalisms for specifying statistical models, such as probabilistic-programming languages, typically consist of two components: a specification of a stochastic process (the prior), and a specification of observations that restrict the…
The completely bounded trace and spectral norms in finite dimensions are shown to be expressible by semidefinite programs. This provides an efficient method by which these norms may be both calculated and verified, and gives alternate…
Determining whether a program terminates is a central problem in computer science. Turing's Halting Problem established termination as undecidable, showing that no algorithm can universally determine termination for all programs and inputs.…
This paper presents a novel approach to constructing finite generating sets for infinitely generated ideals. By integrating algebraic and computational techniques, we provide a method to identify finite generators, demonstrated through…