We study a composition operation on monads, equivalently presented as large equational theories. Specifically, we discuss the existence of tensors, which are combinations of theories that impose mutual commutation of the operations from the component theories. As such, they extend the sum of two theories, which is just their unrestrained combination. Tensors of theories arise in several context...

Abstrac t -The relational model is extended to include nested structures. This extension is formalised using the distinction between a tuple scheme and a relation scheme. The algebra and calculus languages are defined for this model. It is shown that the restricted powerset is a derived operation in the algebra and the full powerset is expressible by a safe forraula in the calculus. Since the f...

Lafont 11] gives an elegant proof of nite model property (fmp) for Multiplicative-Additive Linear Logic (MALL) and suggests it can be adapted to noncommutative linear logics of Abrusci 1]. In 4, 6, 9], fmp for certain fragments of MALL (e.g. BCI, BCII^]) and weaker systems (e.g. the product-free Lambek calculus) has been proven by a diierent method; whereas Lafont uses phase space models and qu...

The convexity of numerical domains such as polyhedra, octagons, intervals and linear equalities enables tractable analysis of software for buffer overflows, null pointer dereferences and floating point errors. However, convexity also causes the analysis to fail in many common cases. Powerset extensions can remedy this shortcoming by considering disjunctions of predicates. Unfortunately, analysi...

For any set-endofunctor T : Set→ Set there exists a largest subcartesian transformation μ to the filter functor F : Set → Set. Thus we can associate with every T -coalgebra A a certain filter-coalgebra AF. Precisely, when T weakly preserves preimages, μ is natural, and when T weakly preserves intersections, μ factors through the covariant powerset functor P, thus providing for every T -coalgebr...

Counterexample-based Refinement for Powerset Domains R. Manevich, J. Field , T. A. Henzinger, G. Ramalingam, and M. Sagiv 1 Tel Aviv University, {rumster,msagiv}@tau.ac.il 2 IBM T.J. Watson Research Center, [email protected] 3 EPFL, [email protected] 4 Microsoft Research India, [email protected] Abstract. Counterexample-guided abstraction refinement (CEGAR) is a powerful technique to scale auto...

Kripke semantics plays a fundamental role for modal logics where it often provides modular semantics allowing a clear treatment of various logics related by the addition of axioms or connectives. Kripke semantics is also the “natural semantics” for classical modal logic in the sense that it is given by the representation theory for modal algebras. The algebraic structure corresponding to a trad...

A set A of positive integers is called a coprime Diophantine powerset if the shifted product ab + 1 of two different elements a and b of A is always a pure power, and the occuring pure powers are all coprime. We prove that each coprime Diophantine powerset A ⊂ {1, . . . , N} has |A| ≤ 8000 logN/ log logN for sufficiently large N . The proof combines results from extremal graph theory with numbe...

Paredaens and Van Gucht proved that the at relational algebra has the same expressive power as the nested relational algebra, as far as queries over at relations and with at results are concerned. We provide a new, very direct proof of this fact using a simulation technique. Our technique is also applied to partially answer a question posed by Suciu and Paredaens regarding the complexity of eva...