%0 Report
%D 2014
%T Towards a Coalgebraic Chomsky Hierarchy
%A Alexandra Silva
%A SergeyGoncharov
%A Stefan Milius
%C Braga, Portugal
%I HASLab/INESC TEC & University of Minho
%X <p>The Chomsky hierarchy plays a prominent role in the foundations of the theoretical computer science relating classes of formal languages of primary importance. In this paper we use recent developments on coalgebraic and monad-based semantics to obtain a generic notion of a T-automaton, where T is a monad, which allows the uniform study of various notions of machines (e.g. finite state machines, multi-stack machines, Turing machines, valence automata, weighted automata). We use the generalized powerset construction to define a generic (trace) semantics for T-automata, and we show by numerous examples that it correctly instantiates for the known classes of machines/languages captured by the Chomsky hierarchy. Moreover, our approach provides new generic techniques for proving expressivity bounds of various machine-based models.</p>
%8 December