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Constrained Horn Clauses (CHCs) are often used in automated program verification. Thus, techniques for (dis-)proving satisfiability of CHCs are a very active field of research. On the other hand, acceleration techniques for computing…
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…
We consider feasibility of linear integer programs in the context of verification systems such as SMT solvers or theorem provers. Although satisfiability of linear integer programs is decidable, many state-of-the-art solvers neglect…
We present a new procedure to infer size bounds for integer programs automatically. Size bounds are important for the deduction of bounds on the runtime complexity or in general, for the resource analysis of programs. We show that our…
Given a program and a time deadline, does the program finish before the deadline when executed on a given platform? With the requirement to produce a test case when such a violation can occur, we refer to this problem as the worst-case…
Chain-of-thought (CoT) reasoning improves large language models (LLMs) on difficult tasks, but it also makes inference expensive because every intermediate step must be generated as a discrete token. Latent reasoning reduces visible token…
We propose a novel acceleration technique for loops operating on arrays. The goal of acceleration is to characterize the transitive closure of loops in a logic which is suitable for automated reasoning. Using the new notion of inductive…
In this paper, we define two particular forms of non-termination, namely loops and binary chains, in an abstract framework that encompasses term rewriting and logic programming. The definition of loops relies on the notion of compatibility…
We introduce a fully automated static analysis that takes a sequential Java bytecode program P as input and attempts to prove that there exists an infinite execution of P. The technique consists in compiling P into a constraint logic…
The safety of our day-to-day life depends crucially on the correct functioning of embedded software systems which control the functioning of more and more technical devices. Many of these software systems are time-critical. Hence,…
This Survey provides an overview of techniques in termination analysis for programs with numerical variables and transitions defined by linear constraints. This subarea of program analysis is challenging due to the existence of undecidable…
Chain-of-Thought (CoT) is a critical technique in enhancing the reasoning ability of Large Language Models (LLMs), and latent reasoning methods have been proposed to accelerate the inefficient token-level reasoning chain. We notice that…
We present abstract acceleration techniques for computing loop invariants for numerical programs with linear assignments and conditionals. Whereas abstract interpretation techniques typically over-approximate the set of reachable states…
The logic embedding tool provides a procedural encoding for non-classical reasoning problems into classical higher-order logic. It is extensible and can support an increasing number of different non-classical logics as reasoning targets.…
Chain-of-Thought (CoT) reasoning successfully enhances the reasoning capabilities of Large Language Models (LLMs), yet it incurs substantial computational overhead for inference. Existing CoT compression methods often suffer from a critical…
A simple linear loop is a simple while loop with linear assignments and linear loop guards. If a simple linear loop has only two program variables, we give a complete algorithm for computing the set of all the inputs on which the loop does…
We consider the termination/non-termination property of a class of loops. Such loops are commonly used abstractions of real program pieces. Second-order logic is a convenient language to express non-termination. Of course, such property is…
Roundoff errors cannot be avoided when implementing numerical programs with finite precision. The ability to reason about rounding is especially important if one wants to explore a range of potential representations, for instance for FPGAs…
Modern software for propositional satisfiability problems gives a powerful automated reasoning toolkit, capable of outputting not only a satisfiable/unsatisfiable signal but also a justification of unsatisfiability in the form of resolution…
Large Language Models (LLMs) have demonstrated strong capabilities in natural language understanding and reasoning. However, their ability to perform exact, deterministic computation remains unclear. In this work, we systematically evaluate…