Grammar semantics, analysis and parsing by abstract interpretation - Cousot, Patrick; Cousot, Radhia (Theoretical computer science, 2011)
We study abstract interpretations of a fixpoint protoderivation semantics defining the maximal derivations of a transitional semantics of context-free grammars akin to pushdown automata. The result is a hierarchy of bottom-up or top-down semantics refining the classical equational and derivational language semantics and including Knuth grammar problems, classical grammar flow analysis algorithms and parsing algorithms.