607 research outputs found
Polynomial equality testing for terms with shared substructures
Sharing of substructures like subterms and subcontexts in terms is a common method for space-efficient representation of terms, which allows for example to represent exponentially large terms in polynomial space, or to represent terms with iterated substructures in a compact form. We present singleton tree grammars as a general formalism for the treatment of sharing in terms. Singleton tree grammars (STG) are recursion-free context-free tree grammars without alternatives for non-terminals and at most unary second-order nonterminals. STGs generalize Plandowski's singleton context free grammars to terms (trees). We show that the test, whether two different nonterminals in an STG generate the same term can be done in polynomial time, which implies that the equality test of terms with shared terms and contexts, where composition of contexts is permitted, can be done in polynomial time in the size of the representation. This will allow polynomial-time algorithms for terms exploiting sharing. We hope that this technique will lead to improved upper complexity bounds for variants of second order unification algorithms, in particular for variants of context unification and bounded second order unification
On Infinite Words Determined by Indexed Languages
We characterize the infinite words determined by indexed languages. An
infinite language determines an infinite word if every string in
is a prefix of . If is regular or context-free, it is known
that must be ultimately periodic. We show that if is an indexed
language, then is a morphic word, i.e., can be generated by
iterating a morphism under a coding. Since the other direction, that every
morphic word is determined by some indexed language, also holds, this implies
that the infinite words determined by indexed languages are exactly the morphic
words. To obtain this result, we prove a new pumping lemma for the indexed
languages, which may be of independent interest.Comment: Full version of paper accepted for publication at MFCS 201
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