Game Semantics is an approach to denotational semantics that has been successful in providing accurate, fully abstract models for various programming languages. It has thereafter been applied, amongst other things, to model checking, access control analysis, information flow analysis, and recently, hardware synthesis.While the roots of modern Game Semantics are sequential, several game models of asynchronous concurrency have since been devised. However, synchronous concurrency has not been considered hitherto.This thesis studies synchronous concurrency in game-like models. The central idea is to investigate deriving such synchronous models from their asynchronous counterparts using round abstraction-a technique that allows aggregating a sequence of computational steps to form a larger, more abstract macro-step.We define round abstraction within a trace-semantic setting that generalises game semantic models. We note that, in general, round abstraction is not compositional. We then identify sufficient conditions to guarantee correct composition, thereby proposing a framework for round abstraction that is sound when applied to synchronous and asynchronous behaviours.

Abstract.A synchronous game semantics-one in which several moves may occur simultaneously-is derived from a conventional (sequential) game semantics using a round abstraction algorithm. We choose the programming language Syntactic Control of Interference and McCusker's fully abstract relational model as a convenient starting point and derive a synchronous game model first by refining the relational semantics into a trace semantics, then applying a round abstraction to it. We show that the resulting model is sound but not fully abstract. This work is practically motivated by applications to hardware synthesis via game semantics.