Related papers: Loops under Strategies ... Continued

We define two transformations from term rewriting systems (TRSs) to context-sensitive TRSs in such a way that termination of the target system implies outermost termination of the original system. In the transformation based on 'context…

Strategy languages enable programmers to compose rewrite rules into strategies and control their application. This is useful in programming languages, e.g., for describing program transformations compositionally, but also in automated…

Higher-order rewriting is a framework in which one can write higher-order programs and study their properties. One such property is termination: the situation that for all inputs, the program eventually halts its execution and produces an…

This paper shows how techniques for linear dynamical systems can be used to reason about the behavior of general loops. We present two main results. First, we show that every loop that can be expressed as a transition formula in linear…

In this paper we propose a language for conveniently defining a wide range of execution strategies for real-time rewrite theories, and provide Maude-strategy-implemented versions of most Real-Time Maude analysis methods, albeit with…

In this paper we establish an automated amortised resource analysis for term rewrite systems. The method is presented in an annotated type system and gives rise to polynomial bounds on the innermost runtime complexity of the analysed term…

In this paper, we reconsider the unfolding-based technique that we have introduced previously for detecting loops in standard term rewriting. We improve it by guiding the unfolding process, using distinguished positions in the rewrite…

Despite the success of test-time scaling, Large Reasoning Models (LRMs) frequently encounter repetitive loops that lead to computational waste and inference failure. In this paper, we identify a distinct failure mode termed Circular…

The application of automatic transformation processes during the formal development and optimization of programs can introduce encumbrances in the generated code that programmers usually (or presumably) do not write. An example is the…

While a mature body of work supports the study of rewriting systems, abstract tools for Probabilistic Rewriting are still limited. In this paper we study the question of uniqueness of the result (unique limit distribution), and develop a…

While loops are present in virtually all imperative programming languages. They are important both for practical reasons (performing a number of iterations not known in advance) and theoretical reasons (achieving Turing completeness). In…

The scope of this work is the constraint-based synthesis of termination arguments for the restricted class of programs called linear lasso programs. A termination argument consists of a ranking function as well as a set of supporting…

Program behavior may depend on parameters, which are either configured before compilation time, or provided at run-time, e.g., by sensors or other input devices. Parametric program analysis explores how different parameter settings may…

Detecting non-termination is crucial for ensuring program correctness and security, such as preventing denial-of-service attacks. While termination analysis has been studied for many years, existing methods have limited scalability and are…

Testing processes usually aim at high coverage, but loops severely limit coverage ambitions since the number of iterations is generally not predictable. Most testing teams address this issue by adopting the extreme solution of limiting…

Large Reasoning Models (LRMs) often suffer from overthinking, generating verbose reasoning traces that compromise both computational efficiency and interpretability. Unlike prior efforts that rely on global length-based rewards, we propose…

Term rewriting systems have a simple syntax and semantics and facilitate proofs of correctness. However, they are not as popular in industry or academia as imperative languages. We define a term rewriting based abstract programming language…

We study the problem of online learning with a notion of regret defined with respect to a set of strategies. We develop tools for analyzing the minimax rates and for deriving regret-minimization algorithms in this scenario. While the…

We present a novel approach to termination analysis. In a first step, the analysis uses a program as a black-box which exhibits only a finite set of sample traces. Each sample trace is infinite but can be represented by a finite lasso. The…

Program analysis and verification require decision procedures to reason on theories of data structures. Many problems can be reduced to the satisfiability of sets of ground literals in theory T. If a sound and complete inference system for…