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In previous work we provided a method for eliminating cuts in non-wellfounded proofs with a local-progress condition, these being the simplest kind of non-wellfounded proofs. The method consisted of splitting the proof into nicely behaved…
Mechanized verification of liveness properties for infinite programs with effects and nondeterminism is challenging. Existing temporal reasoning frameworks operate at the level of models such as traces and automata. Reasoning happens at a…
Proof by coupling is a classical technique for proving properties about pairs of randomized algorithms by carefully relating (or coupling) two probabilistic executions. In this paper, we show how to automatically construct such proofs for…
Resilience is a concept of rising interest in computer science and software engineering. For systems in which correctness w.r.t. a safety condition is unachievable, fast recovery is demanded. We investigate resilience problems of graph…
In real-world phenomena which involve mutual influence or causal effects between interconnected units, equilibrium states are typically represented with cycles in graphical models. An expressive class of graphical models, relational causal…
Many existing tools in nonlinear control theory for establishing stability or safety of a dynamical system can be distilled to the construction of a certificate function that guarantees a desired property. However, algorithms for…
In this report, we show how to use the Simple Fluent Calculus (SFC) to specify generic tracers, i.e. tracers which produce a generic trace. A generic trace is a trace which can be produced by different implementations of a software…
This paper is a brief and informal presentation of cirquent calculus, a novel proof system for resource-conscious logics. As such, it is a refinement of sequent calculus with mechanisms that allow to explicitly account for the possibility…
The two major systems of formal verification are model checking and algebraic model-based testing. Model checking is based on some form of temporal logic such as linear temporal logic (LTL) or computation tree logic (CTL). One powerful and…
Checking the soundness of cyclic induction reasoning for first-order logic with inductive definitions (FOLID) is decidable but the standard checking method is based on an exponential complement operation for B\"uchi automata. Recently, we…
Getting language models to reason correctly about code requires training on data where each reasoning step can be checked. Current synthetic Chain-of-Thought (CoT) training data often consists of plausible-sounding explanations generated by…
We present techniques to prove termination of cycle rewriting, that is, string rewriting on cycles, which are strings in which the start and end are connected. Our main technique is to transform cycle rewriting into string rewriting and…
The notion of clause set cycle abstracts a family of methods for automated inductive theorem proving based on the detection of cyclic dependencies between clause sets. By discerning the underlying logical features of clause set cycles, we…
With the development of real-time networks such as reactive embedded systems, there is a need to compute deterministic performance bounds. This paper focuses on the performance guarantees and stability conditions in networks with cyclic…
This paper discusses limitations of reflexive and diagonal arguments as methods of proof of limitative theorems (e.g. G\"odel's theorem on Entscheidungsproblem, Turing's halting problem or Chaitin-G\"odel's theorem). The fact, that a formal…
Cook and Reckhow 1979 pointed out that NP is not closed under complementation iff there is no propositional proof system that admits polynomial size proofs of all tautologies. Theory of proof complexity generators aims at constructing sets…
Retrieval-augmented generation (RAG) offers an effective approach for addressing question answering (QA) tasks. However, the imperfections of the retrievers in RAG models often result in the retrieval of irrelevant information, which could…
Cirquent calculus is a new proof-theoretic and semantic framework, whose main distinguishing feature is being based on circuits, as opposed to the more traditional approaches that deal with tree-like objects such as formulas or sequents.…
Circular and non-wellfounded proofs have become an increasingly popular tool for metalogical treatments of systems with forms of induction and/or recursion. In this work we investigate the expressivity of a variant CT of G\"odel's system T…
We investigate the cyclic proof theory of extensions of Peano Arithmetic by (finitely iterated) inductive definitions. Such theories are essential to proof theoretic analyses of certain `impredicative' theories; moreover, our cyclic systems…