Deleting String Rewriting Systems Preserve Regularity

Termination Proofs for String Rewriting Systems via Inverse Match-Bounds

“…Corollary 1 ( [11,12]). Every inverse deleting string rewriting system effectively preserves context-free languages.…”

“…In this section we shortly recall definitions and results regarding deleting string rewriting systems [12], a topic that can be traced back to Hibbard [11]. This class of string rewriting systems enjoys a strong decomposition property.…”

“…All these results will be frequently used in the sequel. For proofs and for a description of the decomposition algorithm we refer to [12]. Definition 1.…”

“…In an earlier paper [8,9], we showed that match-bounded string rewriting systems terminate, have linear derivational complexity, and preserve regular languages. A match-bounded system can be encoded into a deleting system [12], and the descendant relation of the latter can be decomposed into components that are known to preserve regular languages.…”

Closure of Hedge-Automata Languages by Hedge Rewriting

“…Let R be the set of all the above right-ground rules and the one-variable rule It has been observed [8] that in several cases, one class of word rewrite system preserves regularity and its symmetric class preserves context-free languages. In this section, we prove a similar result by showing that a restricted case of contextfree HRS, i.e.…”