On Languages Generated by Signed Grammars
\"Omer E\u{g}ecio\u{g}lu (Department of Computer Science, University, of California, Santa Barbara, CA, USA), Benedek Nagy (Department of, Mathematics, Eastern Mediterranean University, North Cyprus, Mersin, Turkey;, Department of Computer Science, Institute of Mathematics
TL;DR
This paper explores languages generated by signed grammars, extending context-free grammars with signed productions, and analyzes their properties using formal series of derivation yields.
Contribution
It introduces signed grammars as a generalization of context-free grammars and studies the properties of the languages they generate using formal series.
Findings
Signed grammars generate new classes of languages.
Formal series of derivation yields characterize these languages.
Properties of these languages are systematically analyzed.
Abstract
We consider languages defined by signed grammars which are similar to context-free grammars except productions with signs associated to them are allowed. As a consequence, the words generated also have signs. We use the structure of the formal series of yields of all derivation trees over such a grammar as a method of specifying a formal language and study properties of the resulting family of languages.
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