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This article describes the *Confluence Framework*, a novel framework for proving and disproving confluence using a divide-and-conquer modular strategy, and its implementation in CONFident. Using this approach, we are able to automatically…
The purpose of this paper is to develop and study recursive proofs of coinductive predicates. Such recursive proofs allow one to discover proof goals in the construction of a proof of a coinductive predicate, while still allowing the use of…
The chase is a fundamental algorithm with ubiquitous uses in database theory. Given a database and a set of existential rules (aka tuple-generating dependencies), it iteratively extends the database to ensure that the rules are satisfied in…
The compactness lemma in programming language theory states that any recursive function can be simulated by a finite unrolling of the function. One important use case it has is in the logical relations proof technique for proving properties…
When programs feature a complex control flow, existing techniques for resource analysis produce cost relation systems (CRS) whose cost functions retain the complex flow of the program and, consequently, might not be solvable into…
Inferring network topology from dynamical observations is a fundamental problem pervading research on complex systems. Here, we present a simple, direct method to infer the structural connection topology of a network, given an observation…
This article presents a reformulation of the Theory of Functional Connections: a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The reformulation presented in this paper exploits…
Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…
Time complexity in rewriting is naturally understood as the number of steps needed to reduce terms to normal forms. Establishing complexity bounds to this measure is a well-known problem in the rewriting community. A vast majority of…
In this paper, we define and study the concept of traceable regressions. These are sequences of regressions in joint or single responses for which a corresponding regression graph captures not only an independence structure but represents,…
We contribute a general apparatus for dependent tactic-based proof refinement in the LCF tradition, in which the statements of subgoals may express a dependency on the proofs of other subgoals; this form of dependency is extremely useful…
Planning is a notoriously difficult computational problem of high worst-case complexity. Researchers have been investing significant efforts to develop heuristics or restrictions to make planning practically feasible. Case-based planning is…
During the last twenty years or so a wide range of realizability interpretations of classical analysis have been developed. In many cases, these are achieved by extending the base interpreting system of primitive recursive functionals with…
We provide here a proof theoretic account of constraint programming that attempts to capture the essential ingredients of this programming style. We exemplify it by presenting proof rules for linear constraints over interval domains, and…
We study the interaction of structural subtyping with parametric polymorphism and recursively defined type constructors. Although structural subtyping is undecidable in this setting, we describe a notion of parametricity for type…
We propose a procedure for automated implicit inductive theorem proving for equational specifications made of rewrite rules with conditions and constraints. The constraints are interpreted over constructor terms (representing data values),…
We derive upper bounds on the complexity of ReLU neural networks approximating the solution of a linear system given the matrix and the right-hand side. We focus on matrices which are symmetric positive definite and sparse, as they appear…
We present decidability results for termination of classes of term rewriting systems modulo permutative theories. Termination and innermost termination modulo permutative theories are shown to be decidable for term rewrite systems (TRS)…
We initiate a study of algorithms with a focus on the computational complexity of individual elements, and introduce the fragile complexity of comparison-based algorithms as the maximal number of comparisons any individual element takes…
Motivated by the problem of finding finite versions of classical incompleteness theorems, we present some conjectures that go beyond ${\bf NP\neq co NP}$. These conjectures formally connect computational complexity with the difficulty of…