Formal Languages - Concatenation and Closure

Closures in Formal Languages: Concatenation, Separation, and Algorithms

We continue our study of open and closed languages. We investigate how the properties of being open and closed are preserved under concatenation. We investigate analogues, in formal languages, of the separation axioms in topological spaces; one of our main results is that there is a clopen partition separating two words if and only if the words commute. We show that we can decide in quadratic t...

Languages with Concatenation ∗

Parsing for Two-staged Languages with Concatenation ∗ Soonho Kong Wontae Choi Kwangkeun Yi Seoul National University {soon,wtchoi,kwang}@ropas.snu.ac.kr Abstract This article, based on Doh, Kim, and Schmidt’s “abstract parsing” technique, presents an abstract interpretation for statically checking the syntax of generated code in two-staged programs. Abstract parsing is a static analysis techniq...

Concatenation and other Closure Properties of Recognizable Languages in Adhesive Categories

We consider recognizable languages of cospans in adhesive categories, of which recognizable graph languages are a special case. We show that such languages are closed under concatenation, i.e. under cospan composition, by providing a concrete construction that creates a concatenation automaton from two given automata. The construction is considerably more complex than the corresponding construc...

Guided Parsing of Range Concatenation Languages

The theoretical study of the range concatenation grammar [RCG] formalism has revealed many attractive properties which may be used in NLP. In particular, range concatenation languages [RCL] can be parsed in polynomial time and many classical grammatical formalisms can be translated into equivalent RCGs without increasing their worst-case parsing time complexity. For example, after translation i...

Automata and formal languages