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Large language models (LLMs) achieve impressive results over various tasks, and ever-expanding public repositories contain an abundance of pre-trained models. Therefore, identifying the best-performing LLM for a given task is a significant…
Constant-rate multi-mode systems (MMS) are hybrid systems with finitely many modes and real-valued variables that evolve over continuous time according to mode-specific constant rates. We introduce a variant of linear temporal logic (LTL)…
We study Linear Temporal Logic Modulo Theories over Finite Traces (LTLfMT), a recently introduced extension of LTL over finite traces (LTLf) where propositions are replaced by first-order formulas and where first-order variables referring…
Model-checking the alternating-time temporal logics ATL and ATL* with incomplete information is undecidable for perfect recall semantics. However, when restricting to memoryless strategies the model-checking problem becomes decidable. In…
Expressing system specifications using Computation Tree Logic (CTL) formulas, formalising programs using Kripke structures, and then model checking the system is an established workflow in program verification and has wide applications in…
Finite model finders give users the ability to specify properties of a system in mathematical logic and then automatically find concrete examples, called solutions, that satisfy the properties. These solutions are often viewed as a key…
Logic programming, as exemplified by datalog, defines the meaning of a program as its unique smallest model: the deductive closure of its inference rules. However, many problems call for an enumeration of models that vary along some set of…
We propose LeanLTL, a unifying framework for linear temporal logics in Lean 4. LeanLTL supports reasoning about traces that represent either infinite or finite linear time. The library allows traditional LTL syntax to be combined with…
Metric temporal logic (MTL) and timed propositional temporal logic (TPTL) are quantitative extensions of linear temporal logic, which are prominent and widely used in the verification of real-timed systems. It was recently shown that the…
In the wake of the recent resurgence of the Datalog language of databases, together with its extensions for ontological reasoning settings, this work aims to bridge the gap between the theoretical studies of DatalogMTL (Datalog extended…
A register automaton is a finite automaton with finitely many registers ranging from an infinite alphabet. Since the valuations of registers are infinite, there are infinitely many configurations. We describe a technique to classify…
Symbolic indefinite integration in Computer Algebra Systems such as Maple involves selecting the most effective algorithm from multiple available methods. Not all methods will succeed for a given problem, and when several do, the results,…
We develop a new numerical method for approximating the infinite time reachable set of strictly stable linear control systems. By solving a linear program with a constraint that incorporates the system dynamics, we compute a polytope with…
Quantified CTL (QCTL) extends the temporal logic CTL with quantifications over atomic propositions. This extension is known to be very expressive: QCTL allows us to express complex properties over Kripke structures (it is as expressive as…
Large language models (LLMs) contain substantial factual knowledge which is commonly elicited by multiple-choice question-answering prompts. Internally, such models process the prompt through multiple transformer layers, building varying…
Proving program termination is typically done by finding a well-founded ranking function for the program states. Existing termination provers typically find ranking functions using either linear algebra or templates. As such they are often…
In this paper, we investigate the problem of synthesizing strategies for linear temporal logic (LTL) specifications that are interpreted over finite traces -- a problem that is central to the automated construction of controllers, robot…
Understanding the internal representations of large language models (LLMs) can help explain models' behavior and verify their alignment with human values. Given the capabilities of LLMs in generating human-understandable text, we propose…
We study monitoring of linear-time arithmetic properties against finite traces generated by an unknown dynamic system. The monitoring state is determined by considering at once the trace prefix seen so far, and all its possible…
SMT solvers have been used successfully as reasoning engines for automated verification and other applications based on automated reasoning. Current techniques for dealing with quantified formulas in SMT are generally incomplete, forcing…