TY  - UNPD
A1  - Schmidt-Schauß, Manfred
T1  - Polynomial equality testing for terms with shared substructures
T2  - Technical report Frank / Johann-Wolfgang-Goethe-Universität, Fachbereich Informatik und Mathematik, Institut für Informatik ; 21
N2  - 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.
T3  - Technical report Frank / Johann-Wolfgang-Goethe-Universität, Fachbereich Informatik und Mathematik, Institut für Informatik - 21 
KW  - Wortproblem
KW  - Baumgrammatiken
KW  - Polynomielles Wortproblem
KW  - sharing
KW  - tree grammars
KW  - polynomial word problem
Y1  - 2005
UR  - http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/3252
UR  - https://nbn-resolving.org/urn:nbn:de:hebis:30-21699
UR  - http://www.ki.informatik.uni-frankfurt.de/papers/schauss/context-cfg-svIB.pdf
EP  - 28
PB  - Johann Wolfgang Goethe-Univ., Fachbereich Informatik und Mathematik, Inst. für Informatik, Research group for Artificial Intelligence and Software Technology
CY  - Frankfurt [am Main]
ER  -