Partially-commutative context-free graphs

This thesis is about an extension of context-free grammars with partial commutation on nonterminal symbols. In particular, we investigate the subclass with transitive dependence relation and the corresponding automaton model: stateless multi-pushdown automata. The results of the thesis are divided into three chapters. The first chapter investigates language expressivity of concerned classes. Roughly speaking, the main result states that in terms of expressivity, partially-commutative contextfree languages are incomparable with two other well-known classes of languages extending context-free languages by a concurrent behaviour. One of these classes is trace closure of context-free languages. The other one is languages generated by context-free grammars with shuffle. The last two chapters concentrate on configuration graphs of partially-commutative context-free grammars rather than on the languages. The second chapter investigates reachability problem for weak multi-pushdown automata, a generalisation of stateless multipushdown automata. Among multiple results discussed in this chapter, the most important ones are NP-completeness for stateless multi-pushdown automata and decidability for weak multi-pushdown automata. The last chapter presents a polynomial-time algorithm deciding bisimilarity in a subclass of partially-commutative context-free graphs that subsumes both context-free graphs and commutative context-free graphs. A specialisation of the algorithm to the class of contextfree graphs works in time O(N polylog(N)), which is the fastest currently known. Finally, we obtain O(N polylog(N)) upper bound in the special case of simple grammars.