Related papers: Saturating Sorting without Sorts
Satisfiability-based automated reasoning is an approach that is being successfully used in software engineering to validate complex software, including for safety-critical systems. Such reasoning underlies many validation activities, from…
In the paper we present results to develop an irreducible theory of complex systems in terms of self-organization processes of prime integer relations. Based on the integers and controlled by arithmetic only the self-organization processes…
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…
Automatic verification of array manipulating programs is a challenging problem because it often amounts to the inference of in ductive quantified loop invariants which, in some cases, may not even be firstorder expressible. In this paper,…
Most ideas about what an algorithm is are very similar. Basic operations are used for transforming objects. The evaluation of internal and external states by relations has impact on the further process. A more precise definition can lead to…
We introduce an algorithm to determine when a sorting operation, such as stack-sort or bubble-sort, outputs a given pattern. The algorithm provides a new proof of the description of West-2-stack-sortable permutations, that is permutations…
Grover's algorithm relies on the superposition and interference of quantum mechanics, which is more efficient than classical computing in specific tasks such as searching an unsorted database. Due to the high complexity of quantum…
For which sets A does there exist a mapping, computed by a total or partial recursive function, such that the mapping, when its domain is restricted to A, is a 1-to-1, onto mapping to $\Sigma^*$? And for which sets A does there exist such a…
We describe simple algebraic and combinatorial characterisations of finite relational core structures admitting finitely many obstructions. As a consequence, we show that it is decidable to determine whether a constraint satisfaction…
We study transformational program logics for correctness and incorrectness that we extend to explicitly handle both termination and nontermination. We show that the logics are abstract interpretations of the right image transformer for a…
Complex logical reasoning tasks require a long sequence of reasoning, which a large language model (LLM) with chain-of-thought prompting still falls short. To alleviate this issue, neurosymbolic approaches incorporate a symbolic solver.…
Optimization algorithms can be interpreted through the lens of dynamical systems as the interconnection of linear systems and a set of subgradient nonlinearities. This dynamical systems formulation allows for the analysis and synthesis of…
Ranking entities such as algorithms, devices, methods, or models based on their performances, while accounting for application-specific preferences, is a challenge. To address this challenge, we establish the foundations of a universal…
Recent work on loglinear models in probabilistic constraint logic programming is applied to first-order probabilistic reasoning. Probabilities are defined directly on the proofs of atomic formulae, and by marginalisation on the atomic…
Qualification has been recently introduced as a generalization of uncertainty in the field of Logic Programming. In this report we investigate a more expressive language for First-Order Functional Logic Programming with Constraints and…
In this thesis we use quasiorders on words to offer a new perspective on two well-studied problems from Formal Language Theory: deciding language inclusion and manipulating the finite automata representations of regular languages. First, we…
Many reasoning, planning, and problem-solving tasks share an intrinsic algorithmic nature: correctly simulating each step is a sufficient condition to solve them correctly. We collect pairs of naturalistic and synthetic reasoning tasks to…
This paper describes a general framework for automatic termination analysis of logic programs, where we understand by ``termination'' the finitenes s of the LD-tree constructed for the program and a given query. A general property of…
Sorting is one of the most used and well investigated algorithmic problem [1]. Traditional postulation supposes the sorting data archived, and the elementary operation as comparisons of two numbers. In a view of appearance of new processors…
We present a generalization of first-order unification to a term algebra where variable indexing is part of the object language. We exploit variable indexing by associating some sequences of variables ($X_0,\ X_1,\ X_2,\dots$) with a…