A b s t r a c t . We define a notion of a Scott family of formulas for a feasible model and give various conditions on a Scott family which imply that two models with the same family are feasibly isomorphic. For example, if A and B possess a common strongly p-time Scott family and both have universe (1}*, then they are p-time isomorphic. These results are applied to the study of permutation str...

MScott (Multi-SCOTT) is a general purpose rst order theorem prover based on McCune's Otter and having the same functionality as Otter. Like its predecessor Scott, it uses a model generator to nd small models of subsets of the clauses generated during proof search. MScott diiers from Scott in that it generates and uses several models simultaneously. This not only improves its coverage of the use...

The aim of this paper is to extend the truth value table oflattice-valued convergence spaces to a more general case andthen to use it to introduce and study the quantale-valued fuzzy Scotttopology in fuzzy domain theory. Let $(L,*,varepsilon)$ be acommutative unital quantale and let $otimes$ be a binary operationon $L$ which is distributive over nonempty subsets. The quadruple$(L,*,otimes,varep...

In this paper, we study in detail the existence and stability of localized pulses in a GiererMeinhardt equation with an additional ‘slow’ nonlinearity. This system is an explicit example of a general class of singularly perturbed, two component reaction-diffusion equations that goes significantly beyond wellstudied model systems such as Gray-Scott and Gierer-Meinhardt. We investigate the existe...

Mathematics of Domains A dissertation presented to the Faculty of the Graduate School of Arts and Sciences of Brandeis University, Waltham, Massachusetts by Michael A. Bukatin Two groups of naturally arising questions in the mathematical theory of domains for denotational semantics are addressed. Domains are equipped with Scott topology and represent data types. Scott continuous functions repre...