TY - GEN
T1 - Complexity of two-variable logic on finite trees
AU - Benaim, Saguy
AU - Benedikt, Michael
AU - Charatonik, Witold
AU - Kieroński, Emanuel
AU - Lenhardt, Rastislav
AU - Mazowiecki, Filip
AU - Worrell, James
PY - 2013
Y1 - 2013
N2 - Verification of properties expressed in the two-variable fragment of first-order logic FO2 has been investigated in a number of contexts. The satisfiability problem for FO2 over arbitrary structures is known to be NEXPTIME-complete, with satisfiable formulas having exponential-sized models. Over words, where FO2 is known to have the same expressiveness as unary temporal logic, satisfiability is again NEXPTIME-complete. Over finite labelled ordered trees FO2 has the same expressiveness as navigational XPath, a popular query language for XML documents. Prior work on XPath and FO2 gives a 2EXPTIME bound for satisfiability of FO2 over trees. This work contains a comprehensive analysis of the complexity of FO2 on trees, and on the size and depth of models. We show that the exact complexity varies according to the vocabulary used, the presence or absence of a schema, and the encoding of labels on trees. We also look at a natural restriction of FO2, its guarded version, GF2. Our results depend on an analysis of types in models of FO 2 formulas, including techniques for controlling the number of distinct subtrees, the depth, and the size of a witness to satisfiability for FO2 sentences over finite trees.
AB - Verification of properties expressed in the two-variable fragment of first-order logic FO2 has been investigated in a number of contexts. The satisfiability problem for FO2 over arbitrary structures is known to be NEXPTIME-complete, with satisfiable formulas having exponential-sized models. Over words, where FO2 is known to have the same expressiveness as unary temporal logic, satisfiability is again NEXPTIME-complete. Over finite labelled ordered trees FO2 has the same expressiveness as navigational XPath, a popular query language for XML documents. Prior work on XPath and FO2 gives a 2EXPTIME bound for satisfiability of FO2 over trees. This work contains a comprehensive analysis of the complexity of FO2 on trees, and on the size and depth of models. We show that the exact complexity varies according to the vocabulary used, the presence or absence of a schema, and the encoding of labels on trees. We also look at a natural restriction of FO2, its guarded version, GF2. Our results depend on an analysis of types in models of FO 2 formulas, including techniques for controlling the number of distinct subtrees, the depth, and the size of a witness to satisfiability for FO2 sentences over finite trees.
UR - http://www.scopus.com/inward/record.url?scp=84880261507&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-39212-2_10
DO - 10.1007/978-3-642-39212-2_10
M3 - منشور من مؤتمر
SN - 9783642392115
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 74
EP - 88
BT - Automata, Languages, and Programming - 40th International Colloquium, ICALP 2013, Proceedings
T2 - 40th International Colloquium on Automata, Languages, and Programming, ICALP 2013
Y2 - 8 July 2013 through 12 July 2013
ER -