23 research outputs found
The Parametric Ordinal-Recursive Complexity of Post Embedding Problems
Post Embedding Problems are a family of decision problems based on the
interaction of a rational relation with the subword embedding ordering, and are
used in the literature to prove non multiply-recursive complexity lower bounds.
We refine the construction of Chambart and Schnoebelen (LICS 2008) and prove
parametric lower bounds depending on the size of the alphabet.Comment: 16 + vii page
Reachability of Communicating Timed Processes
We study the reachability problem for communicating timed processes, both in
discrete and dense time. Our model comprises automata with local timing
constraints communicating over unbounded FIFO channels. Each automaton can only
access its set of local clocks; all clocks evolve at the same rate. Our main
contribution is a complete characterization of decidable and undecidable
communication topologies, for both discrete and dense time. We also obtain
complexity results, by showing that communicating timed processes are at least
as hard as Petri nets; in the discrete time, we also show equivalence with
Petri nets. Our results follow from mutual topology-preserving reductions
between timed automata and (untimed) counter automata.Comment: Extended versio
The Context-Freeness Problem Is coNP-Complete for Flat Counter Systems
International audienceBounded languages have recently proved to be an important class of languages for the analysis of Turing-powerful models. For instance, bounded context-free languages are used to under-approximate the behav-iors of recursive programs. Ginsburg and Spanier have shown in 1966 that a bounded language L ⊆ a * 1 · · · a * d is context-free if, and only if, its Parikh image is a stratifiable semilinear set. However, the question whether a semilinear set is stratifiable, hereafter called the stratifiability problem, was left open, and remains so. In this paper, we give a partial answer to this problem. We focus on semilinear sets that are given as finite systems of linear inequalities, and we show that stratifiability is coNP-complete in this case. Then, we apply our techniques to the context-freeness problem for flat counter systems, that asks whether the trace language of a counter system intersected with a bounded regular language is context-free. As main result of the paper, we show that this problem is coNP-complete