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            <title xml:lang="en">Towards a Coalgebraic Chomsky Hierarchy</title>
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                <title xml:lang="en">Towards a Coalgebraic Chomsky Hierarchy</title>
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                  <title>8th IFIP International Conference on Theoretical Computer Science (TCS)</title>
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                  <date type="end">2014-09-03</date>
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                <editor>Ivan Lanese</editor>
                <editor>Davide Sangiorgi</editor>
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              <p>The Chomsky hierarchy plays a prominent role in the foundations of 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 $\mathbb{T}$-automaton, where $\mathbb{T}$ is a monad, which allows the uniform study of various notions of machines (e.g. finite state machines, multi-stack machines, Turing machines, weighted automata). We use the generalized powerset construction to define a generic (trace) semantics for $\mathbb{T}$-automata, and we show by numerous examples that it correctly instantiates for some known classes of machines/languages captured by the Chomsky hierarchy. Moreover, our approach provides new generic techniques for studying expressivity power of various machine-based models.</p>
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