Results 1 
5 of
5
Searching Constant Width Mazes Captures the AC° Hierarchy
 In Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
, 1997
"... We show that searching a width /' maze is complete for II, i.e., for the /"th level of the AC hierarchy. Equivalently, stconnectivity for width /' grid graphs is complete for II. As an application, we show that there is a data structure solving dynamic stconnectivity for constant width grid gr ..."
Abstract

Cited by 24 (4 self)
 Add to MetaCart
We show that searching a width /' maze is complete for II, i.e., for the /"th level of the AC hierarchy. Equivalently, stconnectivity for width /' grid graphs is complete for II. As an application, we show that there is a data structure solving dynamic stconnectivity for constant width grid graphs with time bound O (log log n) per operation on a random access machine. The dynamic algorithm is derived from the parallel one in an indirect way using algebraic tools.
Relational Reasoning about Contexts
 HIGHER ORDER OPERATIONAL TECHNIQUES IN SEMANTICS, PUBLICATIONS OF THE NEWTON INSTITUTE
, 1998
"... ..."
Syntax and Semantics of the logic ...
, 1997
"... In this paper we study the logic L !! , which is first order logic extended by quantification over functions (but not over relations). We give the syntax of the logic, as well as the semantics in Heyting categories with exponentials. Embedding the generic model of a theory into a Grothendieck t ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
In this paper we study the logic L !! , which is first order logic extended by quantification over functions (but not over relations). We give the syntax of the logic, as well as the semantics in Heyting categories with exponentials. Embedding the generic model of a theory into a Grothendieck topos yields completeness of L !! with respect to models in Grothendieck toposes, which can be sharpened to completeness with respect to Heyting valued models. The logic L !! is the strongest for which Heyting valued completeness is known. Finally, we relate the logic to locally connected geometric morphisms between toposes.
An Elementary Definability Theorem for First Order Logic
"... this paper, we will present a definability theorem for first order logic. This theorem is very easy to state, and its proof only uses elementary tools. To explain the theorem, let us first observe that if M is a model of a theory T in a language L, then, clearly, any definable subset S ae M (i.e., a ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
this paper, we will present a definability theorem for first order logic. This theorem is very easy to state, and its proof only uses elementary tools. To explain the theorem, let us first observe that if M is a model of a theory T in a language L, then, clearly, any definable subset S ae M (i.e., a subset S = fa j M j= '(a)g defined by some formula ') is invariant under all automorphisms of M . The same is of course true for subsets of M
A First Order Modal Logic and its Sheaf Models
"... Abstract: We present a new way of formulating first order modal logic which circumvents the usual difficulties associated with variables changing their reference on moving between states. This formulation allows a very general notion of model (sheaf models). The key idea is the introduction of synta ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Abstract: We present a new way of formulating first order modal logic which circumvents the usual difficulties associated with variables changing their reference on moving between states. This formulation allows a very general notion of model (sheaf models). The key idea is the introduction of syntax for describing relations between individuals in related states. This adds an extra degree of expressiveness to the logic, and also appears to provide a means of describing the dynamic behaviour of computational systems in a way somewhat different from traditional program logics. 1