Mathematical Foundations of Computer Science 

About: Mathematical Foundations of Computer Science is an academic conference. The conference publishes majorly in the area(s): Time complexity & Decidability. Over the lifetime, 2848 publications have been published by the conference receiving 39602 citations.

Graph-theoretic arguments in low-level complexity

Abstract: We have surveyed one approach to understanding complexity issues for certain easily computable natural functions. Shifting graphs have been seen to account accurately and in a unified way for the superlinear complexity of several problems for various restricted models of computation. To attack "unrestricted" models (in the present context combinational circuits or straight-line arithmetic programs,) a first attempt, through superconcentrators, fails to provide any lower bounds although it does give counter-examples to alternative approaches. The notion of rigidity, however, does offer for the first time a reduction of relevant computational questions to noncomputional properties. The "reduction" consists of the conjunction of Corollary 6.3 and Theorem 6.4 which show that "for most sets of linear forms over the reals the stated algebraic and combinatorial reasons account for the fact that they cannot be computed in linear time and depth O(log n) simultaneously." We have outlined some problem areas which our preliminary results raise, and feel that further progress on most of these is humanly feasible. We would be interested in alternative approaches also.

Treewidth: Algorithmic techniques and results

Abstract: This paper gives an overview of several results and techniques for graphs algorithms that compute the treewidth of a graph or that solve otherwise intractable problems when restricted graphs with bounded treewidth more efficiently. Also, several results on graph minors are reviewed.

Full abstraction for a simple parallel programming language

Abstract: In [Plol] a powerdomain was defined which was intended as a kind of analogue of the powerset construction, but for (certain kinds) of cpos. For example the powerdomain~(S±) of the flat cpo Si, formed from a set S, is the set {X ! S~I(X#~) and ((±cX) or X is finite)} with the Egli-Milner ordering : X ~ Y ~ (~x ~ X.~ y ~ Y. x C y) A (~y c Y.3 x e X. x ~ y). E-M This enabled nondeterminism to be modelled by an analogue of set-theoretic union and a denotational semantics for a simple language with parallelism was given, treating parallelism in terms of non-deterministic mergeing of uninterruptible actions. Expected identities such as the associativity and commutativity of the parallel combinator were true in this semantics.

Equivalence notions for concurrent systems and refinement of actions

Abstract: We investigate equivalence notions for concurrent systems. We consider ”linear time” approaches where the system behaviour is characterised as the set of possible runs as well as ”branching time” approaches where the conflict structure of systems is taken into account. We show that the usual interleaving equivalences, and also the equivalences based on steps (multisets of concurrently executed actions) are not preserved by refinement of atomic actions. We prove that ”linear time” partial order semantics, where causality in runs is explicit, is invariant under refinement. Finally, we consider various bisimulation equivalences based on partial orders and show that the strongest one of them is preserved by refinement whereas the others are not.