Immermann, N. (1986). Relational queries computable in polynomial time. Information and Control, 68, 86-104. Home/Search Document Not in Database Summary Related Articles Check |
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Bisimulation, Modal Logic and Model Checking Games - Stirling (1999) (Correct)
.... 3 colourability is given by: 9X: 9Y: 9Z: 2( X [a] X) Y [a] Y ) Z [a] Z) where , which says that every vertex has a unique colour, is 2( X :Y :Z) Y :Z :X) Z :X :Y ) In contrast, modal mu calculus can only express PTIME graph properties (this follows from [17]) Recently Otto showed that an extension of modal mu calculus (with increased xed point arities) exactly captures the PTIME bisimulation closed graph properties [29] We can also contrast M and 2M using games that are extensions of the bisimulation game de ned earlier. These extended games ....
Immermann, N. (1986). Relational queries computable in polynomial time. Information and Control, 68, 86-104.
Games and Modal Mu-Calculus - Stirling (1996) (5 citations) (Correct)
.... = fag, and 3 colourability is given by: 9X: 9Y: 9Z: Phi 2( X [a] X) Y [a] Y ) Z [a] Z) where Phi, which says that every vertex has a unique colour, is 2( X :Y :Z) Y :Z :X) Z :X :Y ) In contrast, modal mu calculus can only express P graph properties (this follows from [10]) First we have Proposition 1 M is a sublogic of 2M . 122 Colin Stirling Proof: There is a straightforward translation of M into 2M . Let Tr be this translation. The important cases are the fixed points: Tr(Z: Phi) 9Z: Z 2(Z Tr( Phi) and Tr(Z: Phi) 8Z: 2(Tr( Phi) Z) Z) 2 When ....
Immermann, N. (1986). Relational queries computable in polynomial time. Information and Control, 68, 86-104.
Directions In Generalized Quantifier Theory - van Benthem, Westerståhl (1994) (Correct)
.... search for a logical characterization for polynomial time computability (PTIME) If we consider models with a given ordering then fixed point logic, FP, provides such a characterization: a property P of finite ordered structures is computable in polynomial time if and only if P is definable in FP (Immermann 1986, Vardi 1982) However, in the general case where the existence of a linear order is not assumed, this characterization fails badly. Indeed the above mentioned quantifier hierarchy result of Hella 1992 implies that there exists no finite set Q of quantifiers such that FP(Q) would characterize all ....
Immermann, N., 1986, Relational queries computable in polynomial time, Information and Control 68, 86--104.
Bisimulation, Model Checking and Other Games - Stirling (Correct)
.... = fag, and 3 colourability is given by: 9X: 9Y: 9Z: Phi 2( X [a] X) Y [a] Y) Z [a] Z) where Phi, which says that every vertex has a unique colour, is 2( X :Y :Z) Y :Z :X) Z :X :Y) In contrast, modal mu calculus can only express PTIME graph properties (this follows from [17]) Proposition 1 M is a sublogic of 2M. Proof: There is a straightforward translation of M into 2M. Let Tr be this translation. The important cases are the fixed points: Tr(Z: Phi) 9Z: Z 2(Z Tr( Phi) and Tr( Z: Phi) 8Z: 2(Tr( Phi) Z) Z) 2 When models are restricted to binary ....
Immermann, N. (1986). Relational queries computable in polynomial time. Information and Control, 68, 86-104.
Model Checking and Other Games - Stirling (1996) (1 citation) (Correct)
....that there is a full alternation depth hierarchy of expressiveness using methods from descriptive set theory [5] Proposition 2 For all n 0, adn ae ad n 1 . This should be contrasted with first order logic and fixed points, FP, over finite models where there is no hierarchy of expressiveness [19]. However this collapse is achieved by increasing the arity of the fixed points. Thus an interesting question is whether there is a hierarchy in the case of FP k , the bounded variable version of FP where all individual variables in any formula are drawn from the set fx 1 ; x k g [35] ....
.... A = fag, and 3 colourability is given by: 9X: 9Y: 9Z: Phi 2( X [a] X) Y [a] Y) Z [a] Z) where Phi, which says that every vertex has a unique colour, is 2( X :Y :Z) Y :Z :X) Z :X :Y) In contrast, modal mu calculus can only express P graph properties (this follows from [19]) Proposition 1 M is a sublogic of 2M. Proof: There is a straightforward translation of M into 2M. Let Tr be this translation. The important cases are the fixed points: Tr(Z: Phi) 9Z: Z 2(Z Tr( Phi) and Tr( Z: Phi) 8Z: 2(Tr( Phi) Z) Z) 2 When models are restricted to binary ....
Immermann, N. (1986). Relational queries computable in polynomial time. Information and Control, 68, 86-104.
A More Expressive Deterministic Query Language With Efficient.. - Gire, Hoang (1996) (Correct)
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N. Immermann. Relational queries computable in polynomial time . Information and Control, 68:86-104, 1986.
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