Quasi-realtime languages

Towards a Coalgebraic Chomsky Hierarchy

“…all recursive ones) by a computationally feasible class of T-automata. This is not surprising in view of the early work on (quasi-)real-time recognizable languages [4], which underlies the proof of Theorem 6.5. We return to this issue in Section 8 where we provide an extension of the present semantics that allows us to capture language classes up to recursively enumerable ones.…”

“…We outline the main distinctions. Instead of quasi-real-time deterministic pda we involve nondeterministic push-down quasi-real-time (NPDQRT) machines from [4]. The transition function δ is thus updated as follows:…”

“…a language accepted by final states can be accepted by empty stack: for m = 1, we obtain standard push-down automata for which equivalence of (i) and (ii) is well-known [29]; for m = 2 this is shown in [40]; for any m > 2 by [4] the languages recognized under (ii) are exactly NTIME(n) and since for quasi-real-time machines the depths of all stacks is linearly bounded, these can be purged in linear time when a final state is reached as required by (i).…”

“…According to [4], we assume that M is real-time, that means that no internal transitions are present.…”

“…We give a formal argument indicating that it is unlikely to capture languages beyond NTIME(n) using coalgebraic (trace) semantics in a straightforward way (i.e., in our case, using the generalized powerset construction) -the phenomenon known before as a property of real-time machines [4]. The requirement to be real-time is an inherent coalgebraic phenomenon of reactivity (or productivity), which restricts the class of behaviors that can be modeled.…”