Coalgebraic Characterizations of Context-Free Languages

Coalgebraic Characterizations of Context-Free Languages

In this article, we provide three coalgebraic characterizations of the class of context-free languages, each based on the idea of adding coalgebraic structure to an existing algebraic structure by specifying output-derivative pairs. Final coalgebra semantics then gives an interpretation function into the final coalgebra of all languages with the usual output and derivative operations. The first...

Context-Free Languages via Coalgebraic Trace Semantics

In this paper we identify context-free grammars as coalgebras. To obtain the associated context-free languages (consisting of only finite-length strings) we introduce a general and novel technique of finite trace semantics for coalgebras. It builds on top of the (possibly infinite) trace semantics introduced earlier by the second author, but extracts only finite behavior. Interestingly the fini...

Characterizations of Context-Sensitive Languages

We give “syntactic” characterizations of context-sensitive languages (CSLs) in terms of some restricted models of symport/antiport P systems. These are the first such characterizations of CSLs in terms of P systems. In particular, we show the following for any language L over a binary alphabet: 1. Let m be any integer ≥ 1. Then L is a CSL if and only if it can be accepted by a restricted sympor...

Two Characterizations of the Context-Sensitive Languages

An n-dimensional bug-automation is generalization of a finite stateacceptor to n-dimensions. With each bug B, we associate the language L(B)which is the set of top rows of n-dimensional rectangular arrays accepted by B.One-dimensional bugs define trivially the regular sets. Two-dimensional bugsdefine precisely the context-sensitive languages, while bugs of dimension 3 orgrea...

Context - Free Languages and