Related papers: Solving Constrained Horn Clauses over ADTs by Fini…
Automated reasoners, such as SAT/SMT solvers and first-order provers, are becoming the backbones of rigorous systems engineering, being used for example in applications of system verification, program synthesis, and cybersecurity.…
An inductive theorem proving method for constrained term rewriting systems, which is based on rewriting induction, needs a decision procedure for reduction-completeness of constrained terms. In addition, the sufficient complete property of…
We present semantic correctness proofs of automatic differentiation (AD). We consider a forward-mode AD method on a higher-order language with algebraic data types and we characterise it as the unique structure-preserving macro given a…
For any first order theory T we construct a Boolean valued model M, in which precisely the T--provable formulas hold, and in which every (Boolean valued) subset which is invariant under all automorphisms of M is definable by a first order…
Decision tree models, including random forests and gradient-boosted decision trees, are widely used in machine learning due to their high predictive performance. However, their complex structures often make them difficult to interpret,…
Many recent analyses for conventional imperative programs begin by transforming programs into logic programs, capitalising on existing LP analyses and simple LP semantics. We propose using logic programs as an intermediate program…
We consider a class of formula equations in first-order logic, Horn formula equations, which are defined by a syntactic restriction on the occurrences of predicate variables. Horn formula equations play an important role in many…
Complex networks are everywhere. They appear for example in the form of biological networks, social networks, or computer networks and have been studied extensively. Efficient algorithms to solve problems on complex networks play a central…
This paper considers finite-automata based algorithms for handling linear arithmetic with both real and integer variables. Previous work has shown that this theory can be dealt with by using finite automata on infinite words, but this…
First-order automatic differentiation is a ubiquitous tool across statistics, machine learning, and computer science. Higher-order implementations of automatic differentiation, however, have yet to realize the same utility. In this paper I…
We consider the problem of automatically proving resource bounds. That is, we study how to prove that an integer-valued resource variable is bounded by a given program expression. Automatic resource-bound analysis has recently received…
We provide a denotational semantics for first-order logic that captures the two-level view of the computation process typical for constraint programming. At one level we have the usual program execution. At the other level an automatic…
We show how the complexity of higher-order functional programs can be analysed automatically by applying program transformations to a defunctionalized versions of them, and feeding the result to existing tools for the complexity analysis of…
Liveness properties are traditionally proven using a ranking function that maps system states to some well-founded set. Carrying out such proofs in first-order logic enables automation by SMT solvers. However, reasoning about many natural…
Catamorphisms are functions that are recursively defined on list and trees and, in general, on Algebraic Data Types (ADTs), and are often used to compute suitable abstractions of programs that manipulate ADTs. Examples of catamorphisms…
Sets with atoms serve as an alternative to ZFC foundations for mathematics, where some infinite, though highly symmetric sets, behave in a finitistic way. Therefore, one can try to carry over analysis of the classical algorithms from finite…
In this paper, an Artificial Neural Network (ANN) technique is developed to find solution of celebrated Fractional order Differential Equations (FDE). Compared to integer order differential equation, FDE has the advantage that it can better…
We give an algebraic characterization of the tree languages that are defined by logical formulas using certain Lindstr\"om quantifiers. An important instance of our result concerns first-order definable tree languages. Our characterization…
The use of temporal logics has long been recognised as a fundamental approach to the formal specification and verification of reactive systems. In this paper, we take on the problem of automatically verifying a temporal property, given by a…
Saturation-style automated theorem provers (ATPs) based on the given clause procedure are today the strongest general reasoners for classical first-order logic. The clause selection heuristics in such systems are, however, often evaluating…