19 research outputs found
Greibach Normal Form in Algebraically Complete Semirings
We give inequational and equational axioms for semirings with a fixed-point operator and formally develop a fragment of the theory of context-free languages. In particular, we show that Greibach's normal form theorem depends only on a few equational properties of least pre-fixed-points in semirings, and elimination of chain- and deletion rules depend on their inequational properties (and the idempotency of addition). It follows that these normal form theorems also hold in non-continuous semirings having enough fixed-points
Coalgebraic characterizations of context-free languages
Article / Letter to editorLeiden Inst Advanced Computer Science
Context-free languages, coalgebraically
We give a coalgebraic account of context-free languages using the
functor for deterministic automata over an
alphabet , in three different but equivalent ways: (i) by viewing
context-free grammars as -coalgebras; (ii) by defining a
format for behavioural differential equations (w.r.t. ) for
which the unique solutions are precisely the context-free languages; and
(iii) as the -coalgebra of generalized regular expressions in
which the Kleene star is replaced by a unique fixed point operator. In
all cases, semantics is defined by the unique homomorphism into the
final coalgebra of all languages, thus paving the way for coinductive
proofs of context-free language equivalence. Furthermore, the three
characterizations are elementary to the extent that they can serve as
the basis for the definition of a general coalgebraic notion of
context-freeness, which we see as the ultimate long-term goal of the
present study