Related papers: On Propositional Program Equivalence (extended abs…
One of my recent papers transforms an NP-Complete problem into the question of whether or not a feasible real solution exists to some Linear Program. The unique feature of this Linear Program is that though there is no explicit bound on the…
We generalise the notion of separable equivalence, originally presented by Linckelmann (2011), to an equivalence relation on additive categories. We use this generalisation to show that from an initial equivalence between two algebras we…
Determining whether a program terminates is a central problem in computer science. Turing's Halting Problem established termination as undecidable, showing that no algorithm can universally determine termination for all programs and inputs.…
We propose a notion of quantum control in a quantum programming language which permits the superposition of finitely many quantum operations without performing a measurement. This notion takes the form of a conditional construct similar to…
We deal with linear programming problems involving absolute values in their formulations, so that they are no more expressible as standard linear programs. The presence of absolute values causes the problems to be nonconvex and nonsmooth,…
Programs with a continuous state space or that interact with physical processes often require notions of equivalence going beyond the standard binary setting in which equivalence either holds or does not hold. In this paper we explore the…
For models of concurrent and distributed systems, it is important and also challenging to establish correctness in terms of safety and/or liveness properties. Theories of distributed systems consider equivalences fundamental, since they (1)…
A logic program is an executable specification. For example, merge sort in pure Prolog is a logical formula, yet shows creditable performance on long linked lists. But such executable specifications are a compromise: the logic is distorted…
When a problem has more than one solution, it is often important, depending on the underlying context, to enumerate (i.e., to list) them all. Even when the enumeration can be done in polynomial delay, that is, spending no more than…
We consider the decidability of the verification problem of programs \emph{modulo axioms} --- that is, verifying whether programs satisfy their assertions, when the functions and relations it uses are assumed to interpreted by arbitrary…
A conic program is the problem of optimizing a linear function over a closed convex cone intersected with an affine preimage of another cone. We analyse three constraint qualifications, namely a Closedness CQ, Slater CQ, and Boundedness CQ…
Computability logic is a formal theory of computational tasks and resources. Its formulas represent interactive computational problems, logical operators stand for operations on computational problems, and validity of a formula is…
We present an extension to the $\mathtt{mathlib}$ library of the Lean theorem prover formalizing the foundations of computability theory. We use primitive recursive functions and partial recursive functions as the main objects of study, and…
Interpolation is an important property of classical and many non classical logics that has been shown to have interesting applications in computer science and AI. Here we study the Interpolation Property for the propositional version of the…
Prioritized default reasoning has illustrated its rich expressiveness and flexibility in knowledge representation and reasoning. However, many important aspects of prioritized default reasoning have yet to be thoroughly explored. In this…
Defeasible logic is a rule-based nonmonotonic logic, with both strict and defeasible rules, and a priority relation on rules. We show that inference in the propositional form of the logic can be performed in linear time. This contrasts…
This paper presents an example of formal reasoning about the semantics of a Prolog program of practical importance (the SAT solver of Howe and King). The program is treated as a definite clause logic program with added control. The logic…
TopKAT is the algebraic theory of Kleene algebra with tests (KAT) extended with a top element. Compared to KAT, one pleasant feature of TopKAT is that, in relational models, the top element allows us to express the domain and codomain of a…
The termination problem for affine programs over the integers was left open in\cite{Braverman}. For more that a decade, it has been considered and cited as a challenging open problem. To the best of our knowledge, we present here the most…
We present and study new definitions of universal and programmable universal unary functions and consider a new simplicity criterion: almost decidability of the halting set. A set of positive integers S is almost decidable if there exists a…