Related papers: Non-Termination in Term Rewriting and Logic Progra…
Recursive relational specifications are commonly used to describe the computational structure of formal systems. Recent research in proof theory has identified two features that facilitate direct, logic-based reasoning about such…
Termination of programs, i.e., the absence of infinite computations, ensures the existence of normal forms for all initial expressions, thus providing an essential ingredient for the definition of a normalization semantics for functional…
Logic programming, as exemplified by datalog, defines the meaning of a program as its unique smallest model: the deductive closure of its inference rules. However, many problems call for an enumeration of models that vary along some set of…
There exist several results on deciding termination and computing runtime bounds for triangular weakly non-linear loops (twn-loops). We show how to use results on such subclasses of programs where complexity bounds are computable within…
Formalisms based on temporal logics interpreted over finite strict linear orders, known in the literature as finite traces, have been used for temporal specification in automated planning, process modelling, (runtime) verification and…
We consider the problem of directly optimizing a non-linear function of an outcome, where this outcome itself is the sum of many small contributions. The non-linearity of the function means that the problem is not equivalent to the…
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…
We propose a way to unify two approaches of non-cloning in quantum lambda-calculi: logical and algebraic linearities. The first approach is to forbid duplicating variables, while the second is to consider all lambda-terms as…
We propose a notion of complexity for oriented conditional term rewrite systems satisfying certain restrictions. This notion is realistic in the sense that it measures not only successful computations, but also partial computations that…
Rewriting Induction (RI) is a method to prove inductive theorems, originating from equational reasoning. By using Logically Constrained Simply-typed Term Rewriting Systems (LCSTRSs) as an intermediate language, rewriting induction becomes a…
Essentially, in a reversible programming language, for each forward computation from state $S$ to state $S'$, there exists a constructive method to go backwards from state $S'$ to state $S$. Besides its theoretical interest, reversible…
We give extensional and intensional characterizations of functional programs with nondeterminism: as structure preserving functions between biorders, and as nondeterministic sequential algorithms on ordered concrete data structures which…
Binary semirings such as the tropical, log, and probability semirings form a core algebraic tool in classical and modern neural inference systems, supporting tasks like Viterbi decoding, dynamic programming, and probabilistic reasoning.…
Pull-tabbing is an evaluation approach for functional logic computations, based on a graph transformation recently proposed, which avoids making irrevocable non-deterministic choices that would jeopardize the completeness of computations.…
The clone of term operations of an algebraic structure consists of all operations that can be expressed by a term in the language of the structure. We consider bounds for the length and the height of the terms expressing these functions,…
We start by defining an approach to non-monotonic probabilistic reasoning in terms of non-monotonic categorical (true-false) reasoning. We identify a type of non-monotonic probabilistic reasoning, akin to default inheritance, that is…
We present a new kind of nontermination argument, called geometric nontermination argument. The geometric nontermination argument is a finite representation of an infinite execution that has the form of a sum of several geometric series.…
This paper is devoted to the extraction of entities and semantic relations between them from scientific texts, where we consider scientific terms as entities. In this paper, we present a dataset that includes annotations for two tasks and…
Program equivalence is the fulcrum for reasoning about and proving properties of programs. For noninterference, for example, program equivalence up to the secrecy level of an observer is shown. A powerful enabler for such proofs are logical…
Programs written in dynamic languages make heavy use of features --- run-time type tests, value-indexed dictionaries, polymorphism, and higher-order functions --- that are beyond the reach of type systems that employ either purely syntactic…