The paper presents a high-level declarative language CO4 for describing constraint systems. The language includes user-defined algebraic data types and recursive functions defined by pattern matching, as well as higher-order and polymorphic types. This language comes with a compiler that transforms a high-level constraint system into a satisfiability problem in propositional logic. This is moti...

In this paper we define a sequential composition for arbitrary co-algebras in a Dedekind category. We show some basic algebraic properties of this operation up to bisimulation. Furthermore, we consider certain recursive equations and provide an explicit solution, i.e., a solution not based on an iterative process.

In this paper sets of labelled partial orders are employed as fundamental mathematical entities for modelling nondeterministic and concurrent processes thereby obtaining so-called noninterleaving semantics. Based on closures of sets of labelled partial orders, a simple recursive algebraic language with refinement is given denotational models fully abstract w.r.t. corresponding behaviourally mot...

Several algebraic machine-independant characterizations of computable functions over the reals have been obtained recently. In particular nice connections between the class of computable functions (and some of its sub and sup-classes) over the reals and algebraically defined (suband sup-) classes of R-recursive functions à la Moore 96 have been obtained. We provide in this paper a framework tha...

SYLLABUS A range of topics for the course follows. 1. Algebraic theories: universal algebra; equational logic; soundness and completeness; theory translations and constructions. 2. Algebras: initial algebras; induction principle; recursive domain equations; free algebras. 3. Presheaves: cartesian closure; essential geometric morphisms; free cocompletions; Kan extensions; coends. 4. Simply typed...

This paper provides a primer in quantum field theory (QFT) based on Hopf algebra and describes new Hopf algebraic constructions inspired by QFT concepts. The following QFT concepts are introduced: chronological products, S-matrix, Feynman diagrams, connected diagrams, Green functions, renormalization. The use of Hopf algebra for their definition allows for simple recursive derivations and lead ...

Interactive proofs of correctness of pointer-manipulating programs tend to be difficult. We propose an approach that integrates shape analysis and interactive theorem proving, namely TVLA and KIV. The approach uses shape analysis to automatically discharge proof obligations for various data structure properties, such as “acyclicity”. We verify the main operations of B trees by decomposition of ...

Completely iterative theories of Calvin Elgot formalize (potentially infinite) computations as solutions of recursive equations. One of the main results of Elgot and his coauthors is that infinite trees form a free completely iterative theory. Their algebraic proof of this result is extremely complicated. We present completely iterative algebras as a new approach to the description of free comp...

We give upper bounds for the differential Nullstellensatz in the case of ordinary systems of differential algebraic equations over the field of complex numbers. Let x be a set of n differential variables, f a finite family of differential polynomials in the ring C{x} and f ∈ C{x} another polynomial which vanishes at every solution of the differential equation system f = 0 in any differentially ...