Related papers: A Type-Based HFL Model Checking Algorithm
An efficient and flexible engine for computing fixed points is critical for many practical applications. In this paper, we firstly present a goal-directed fixed point computation strategy in the logic programming paradigm. The strategy…
Large language models (LLMs) have recently demonstrated remarkable progress in formal theorem proving. Yet their ability to serve as practical assistants for mathematicians, filling in missing steps within complex proofs, remains…
We investigate infinitary wellfounded systems for linear logic with fixed points, with transfinite branching rules indexed by some closure ordinal $\alpha$ for fixed points. Our main result is that provability in the system for some…
This paper tackles the problem of formulating and proving the completeness of focused-like proof systems in an automated fashion. Focusing is a discipline on proofs which structures them into phases in order to reduce proof search…
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…
In the last two decades, there has been much progress on model checking of both probabilistic systems and higher-order programs. In spite of the emergence of higher-order probabilistic programming languages, not much has been done to…
Satisfiability checking for Linear Temporal Logic (LTL) is a fundamental step in checking for possible errors in LTL assertions. Extant LTL satisfiability checkers use a variety of different search procedures. With the sole exception of LTL…
We propose a verified approach to the formal verification of timed properties using model-checking techniques. We focus on properties expressed using real-time specification patterns, which can be viewed as a subset of timed temporal logics…
Type checking algorithms and theorem provers rely on unification algorithms. In presence of type families or higher-order logic, higher-order (pre)unification (HOU) is required. Many HOU algorithms are expressed in terms of…
Enhancing the mathematical reasoning capabilities of LLMs has garnered significant attention in both the mathematical and computer science communities. Recent works have made substantial progress in both Natural Language (NL) reasoning and…
I consider the following generic scenario: an abstract model M of some 'real' system is only partially presented, or partially known to us, and we have to ensure that the actual system satisfies a given specification, formalised in some…
Several recently devised machine learning (ML) algorithms have shown improved accuracy for various predictive problems. Model searches, which explore to find an optimal ML algorithm and hyperparameter values for the target problem, play a…
Mixed integer linear programming (MILP) is a powerful representation often used to formulate decision-making problems under uncertainty. However, it lacks a natural mechanism to reason about objects, classes of objects, and relations.…
Most modal logics such as S5, LTL, or ATL are extensions of Modal Logic K. While the model checking problems for LTL and to a lesser extent ATL have been very active research areas for the past decades, the model checking problem for the…
High-level synthesis (HLS) transforms an algorithmic description of hardware from a higher abstraction (e.g., C/C++) into a register-transfer level (RTL) design, offering reduced development time and greater flexibility in design space…
We study the topological $\mu$-calculus, based on both Cantor derivative and closure modalities, proving completeness, decidability and FMP over general topological spaces, as well as over $T_0$ and $T_D$ spaces. We also investigate…
As High-Performance Computing (HPC) systems strive towards the exascale goal, failure rates both at the hardware and software levels will increase significantly. Thus, detecting and classifying faults in HPC systems as they occur and…
Subtyping is a crucial ingredient of session type theory and its applications, notably to programming language implementations. In this paper, we study effective ways to check whether a session type is a subtype of another by applying a…
This paper investigates first-order game logic and first-order modal mu-calculus, which extend their propositional modal logic counterparts with first-order modalities of interpreted effects such as variable assignments. Unlike in the…
Large Language Models (LLMs) demonstrate impressive mathematical reasoning abilities, but their solutions frequently contain errors that cannot be automatically checked. Formal theorem proving systems such as Lean 4 offer automated…