S. Abiteboul, V. Vianu, Generic Computation and Its Complexity, Proc. 23rd ACM Symp. on Theory of Computing (1991), 209-219.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....in the present context lies in the fact that it allows While recursion over A of polynomial time complexity. As observed above, FP only captures While recursion of time complexity polynomial in the index with respect to L k equivalence for some k rather than in the size of the structure; see [1, 2, 5] for further analysis. The main theorem states that the gap in recursive power between FP and FP cannot be bridged by the adjunction of simple structural properties: Theorem 10 (Main Theorem) Let Q be a family based on simple invariants. Then FP(Q) does not contain PTime, in fact even FP(Q) ....

S. Abiteboul, V. Vianu, Generic Computation and Its Complexity, Proc. 23rd ACM Symp. on Theory of Computing (1991), 209-219

....inputs give rise to isomorphic computations. Models of computation satisfying this invariance condition are called generic in the literature. They have been studied in the context of foundational issues, e.g. GL 81] and also in the context of finite model theory and database theory, e.g. AV 91] There is considerable interest in complexity analysis related to natural generic models of computation for several reasons: i) The classical complexity classes, e.g. based on Turing machines, were obviously intended to deal with strings, i.e. with linearly ordered structures for inputs. ii) ....

S. Abiteboul, V. Vianu, Generic Computation and Its Complexity, Proc. 23rd ACM Symp. on Theory of Computing (1991), 209--219

....H and K, so that we find that the C 2 and L 2 fragments of Ptime are recursively enumerable and admit a normal form of the indicated kind. We do get a little more than that even, owing to the manner in which we obtain these canonizations. Through the work of Abiteboul and Vianu, [1], L k is known to possess concise invariants, that characterize structures up to j L k . These Ptime functors I k map finite structures to linearly ordered structures of suitable type, such that for any two finite structures A and A 0 , I k (A) I k (A 0 ) A j L k A 0 . ....

....I k map finite structures to linearly ordered structures of suitable type, such that for any two finite structures A and A 0 , I k (A) I k (A 0 ) A j L k A 0 . Furthermore, fixed point queries exactly correspond to the Ptime properties of the images under the I k . See [1], and in particular [4] and [5] for the logical interpretation and the connection with L k . For C k analogous invariants I k C are introduced in [13] and applied to the analysis of fixed point logic with counting, see also [6] In either case, the invariants can be pictured as ordered ....

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S. Abiteboul, V. Vianu, Generic Computation and Its Complexity, Proc. 23rd ACM Symp. on Theory of Computing (1991), 209-219.

....Ptime if and only if can(Q) Phi can(A; a) fi fi a 2 Q A Psi is definable in LFP over CAN fin . In formulae this may be summed up more suggestively as Ptime ML1 j LFP ffi can: The above method of constructing inductively an ordering of the types was conceived by Abiteboul and Vianu [1] in the setting of relational computation, where it became instrumental in their fundamental investigation of least versus partial fixed point. The logical and game theoretic formulations, on which the present treatment is modeled, were abstracted and applied to bounded variable logics in [11, 14, ....

S. Abiteboul and V. Vianu, Generic computation and its complexity, Proc. 23rd ACM Symp. on Theory of Computing, 1991, pp. 209--219.

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S. Abiteboul, V. Vianu, Generic Computation and Its Complexity, Proc. 23rd ACM Symp. on Theory of Computing (1991), 209-219.

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