Abstract. According to the functional approach to language evolution (inspired by cognitive linguistics and construction grammar), grammar arises to deal with issues in communication among autonomous agents, particularly maximisation of communicative success and expressive power and minimisation of cognitive effort. Experiments in the emergence of grammar should hence start from a simulation of communicative exchanges between embodied agents, and then show how a particular issue that arises can be solved or partially solved by introducing more grammar. This paper shows a case study of this approach, focusing on the issue of search during parsing. Multiple hypotheses arise in parsing when the same syntactic pattern can be used for multiple purposes or when one syntactic pattern partly overlaps with another one. It is well known that syntactic ambiguity rapidly leads to combinatorial explosions and hence an increase in memory use and processing power, possibly to a point where the senten...