Related papers: Time-complexity semantics for feasible affine recu…
All current investigations to analyze the derivational complexity of term rewrite systems are based on a single termination method, possibly preceded by transformations. However, the exclusive use of direct criteria is problematic due to…
Abductive reasoning is a non-monotonic formalism stemming from the work of Peirce. It describes the process of deriving the most plausible explanations of known facts. Considering the positive version asking for sets of variables as…
One of the aims of Implicit Computational Complexity is the design of programming languages with bounded computational complexity; indeed, guaranteeing and certifying a limited resources usage is of central importance for various aspects of…
Region-based type systems are a powerful tool for various kinds of program analysis. We introduce a new inference algorithm for region types based on an abstract notion of environment transformation. It analyzes the code of a method only…
Answer set programming - the most popular problem solving paradigm based on logic programs - has been recently extended to support uninterpreted function symbols. All of these approaches have some limitation. In this paper we propose a…
This paper describes an abstract machine for linguistic formalisms that are based on typed feature structures, such as HPSG. The core design of the abstract machine is given in detail, including the compilation process from a high-level…
Approximation Fixpoint Theory (AFT) is a powerful theory covering various semantics of non-monotonic reasoning formalisms in knowledge representation such as Logic Programming and Answer Set Programming. Many semantics of such non-monotonic…
The OpenAI o1-series models have demonstrated that leveraging long-form Chain of Thought (CoT) can substantially enhance performance. However, the recursive thinking capabilities of Large Language Models (LLMs) remain limited, particularly…
Fully automatic worst-case complexity analysis has a number of applications in computer-assisted program manipulation. A classical and powerful approach to complexity analysis consists in formally deriving, from the program syntax, a set of…
In high-complexity abstract reasoning, a system must infer a latent rule from a few examples or structured observations and apply it to unseen instances. LLMs can express such rules as programs, but ordinary conversation-based refinement is…
In this paper, we propose an additionsubtraction twin-gated recurrent network (ATR) to simplify neural machine translation. The recurrent units of ATR are heavily simplified to have the smallest number of weight matrices among units of all…
This paper studies the limits of recursive classifications in proof theory and program extraction, using the refined $A$-translation as a central example. The refined $A$-translation, due to Berger, Buchholz, and Schwichtenberg, is based on…
Algorithms for partition refinement are actively studied for a variety of systems, often with the optimisation called Hopcroft's trick. However, the low-level description of those algorithms in the literature often obscures the essence of…
Recent work has shown that the computations of Transformers can be simulated in the RASP family of programming languages. These findings have enabled improved understanding of the expressive capacity and generalization abilities of…
Hofmann (1999) introduced the functional programming language LFPL to characterize the functions computable in polynomial time using an affine type system. LFPL enables a natural programming style, including nested recursion, and has…
Based on a previously developed recursive approach for calculating the short-time expansion of the propagator for systems with time-independent potentials and its time-dependent generalization for simple single-particle systems, in this…
Tiny Recursive Models (TRM) were proposed as a parameter-efficient alternative to large language models for solving Abstraction and Reasoning Corpus (ARC) style tasks. The original work reports strong performance and suggests that recursive…
We investigate feasible computation over a fairly general notion of data and codata. Specifically, we present a direct Bellantoni-Cook-style normal/safe typed programming formalism, RS1, that expresses feasible structural recursions and…
Tail recursive functions allow for a wider range of optimisations than general recursive functions. For this reason, much research has gone into the transformation and optimisation of this family of functions, in particular those written in…
We introduce Associative Commutative Distributive Term Rewriting (ACDTR), a rewriting language for rewriting logical formulae. ACDTR extends AC term rewriting by adding distribution of conjunction over other operators. Conjunction is vital…