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GNU Prolog is a general-purpose implementation of the Prolog language, which distinguishes itself from most other systems by being, above all else, a native-code compiler which produces standalone executables which don't rely on any…
Universality is one of the most important ideas in computability theory. There are various criteria of simplicity for universal Turing machines. Probably the most popular one is to count the number of states/symbols. This criterion is more…
Runtime verification is an effective automated method for specification-based offline testing and analysis as well as online monitoring of complex systems. The specification language is often a variant of regular expressions or a popular…
We discuss the possibility of constructing a function that validates the definition or not definition of the partial recursive functions of one variable. This is a topic in computability theory, which was first approached by Alan M. Turing…
This paper presents results from the development and evaluation of a deductive verification benchmark consisting of 26 unmodified Linux kernel library functions implementing conventional memory and string operations. The formal contract of…
By algorithmic metatheorems for a model checking problem P over infinite-state systems we mean generic results that can be used to infer decidability (possibly complexity) of P not only over a specific class of infinite systems, but over a…
A notable feature of the TTE approach to computability is the representation of the argument values and the corresponding function values by means of infinitistic names. Two ways to eliminate the using of such names in certain cases are…
The mainstream machine learning paradigms for NLP often work with two underlying presumptions. First, the target task is predefined and static; a system merely needs to learn to solve it exclusively. Second, the supervision of a task mainly…
This paper is concerned with the expressivity and denotational semantics of a functional higher-order reversible programming language based on Theseus. In this language, pattern-matching is used to ensure the reversibility of functions. We…
Determining the degree of inherent parallelism in classical sequential algorithms and leveraging it for fast parallel execution is a key topic in parallel computing, and detailed analyses are known for a wide range of classical algorithms.…
This paper talk about the complexity of computation by Turing Machine. I take attention to the relation of symmetry and order structure of the data, and I think about the limitation of computation time. First, I make general problem named…
In reductive proof search, proofs are naturally generalized by solutions, comprising all possibly infinite structures generated by locally correct, bottom-up application of inference rules. We propose an extension of the Curry-Howard…
The rise of code pre-trained models has significantly enhanced various coding tasks, such as code completion, and tools like GitHub Copilot. However, the substantial size of these models, especially large models, poses a significant…
Random testing has proven to be an effective technique for compiler validation. However, the debugging of bugs identified through random testing presents a significant challenge due to the frequent occurrence of duplicate test programs that…
Coinduction refers to both a technique for the definition of infinite streams, so-called codata, and a technique for proving the equality of coinductively specified codata. This article first reviews coinduction in declarative programming.…
Recently, various natural algorithmic problems have been shown to be $\exists \mathbb{R}$-complete. The reduction relied in many cases on the $\exists \mathbb{R}$-completeness of the problem ETR-INV, which served as a useful intermediate…
This work establishes a rigorous theoretical foundation for analyzing deep learning systems by leveraging Infinite Time Turing Machines (ITTMs), which extend classical computation into transfinite ordinal steps. Using ITTMs, we reinterpret…
Neural language models (LMs) have achieved impressive results on various language-based reasoning tasks by utilizing latent knowledge encoded in their own pretrained parameters. To make this reasoning process more explicit, recent works…
In this paper, we consider a new direction of computation, which we call computation with large advice. We mainly consider constant space computation with large advice in Turing machines, and prove the following facts: (i) The class of…
LLMs demonstrate strong performance on code benchmarks, yet consistent reasoning across forward and backward execution remains elusive. We present RoundTripCodeEval (RTCE), a benchmark of four code execution reasoning tasks that evaluates…