T. Feder. Stable networks and product graphs. PhD thesis, Stanford University, 1981.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....logic augmented with the noninflationary fixpoint formation rule for arbitrary 1st order formulas. Note that NFP fixpoint logic is an extension of IFP . While IFP formulas can be evaluated in polynomial time, NFP can express PSPACE complete problems, such as the network convergence problem [Fed81]. Noninflationary fixpoint logic was introduced by Abiteboul and Vianu [AV89] who called it partial fixpoint logic) In particular, they observed that noninflationary fixpoint logic coincides with the query language RQL introduced in [CH82] and studied further in [Var82] It follows that NFP ....

T. Feder. Stable networks and product graphs. PhD thesis, Stanford University, 1981.

....is an extension of IFP . While IFP formulas can be evaluated 5 Actually, it is shown in [AV90] that there is no loss of generality in restricting attention to converging 1st order operators. in polynomial time, NFP can express PSPACE complete problems, such as the network convergence problem [Fed91]. Noninflationary fixpoint logic was introduced by Abiteboul and Vianu [AV91a] who called it partial fixpoint logic) In particular, they observed that noninflationary fixpoint logic coincides with the query language RQL introduced in [CH82] and studied further in [Var82] It follows that NFP ....

T. Feder. Stable networks and product graphs. PhD thesis, Stanford University, 1991.

....in restricting attention to converging 1st order operators, i.e. to operators such that Phi m0 = Phi m0 1 for some integer m 0 . polynomial time, NFP formulas can be evaluated in polynomial space and can express PSPACE complete problems, such as the network convergence problem [Fed91]. Noninflationary fixpoint logic was introduced by Abiteboul and Vianu [AV91a] who called it partial fixpoint logic) In particular, they observed that noninflationary fixpoint logic coincides with the query language RQL introduced in [CH82] and studied further in [Var82] It follows that NFP ....

T. Feder. Stable networks and product graphs. PhD thesis, Stanford University, 1991.

....logic augmented with the noninflationary fixpoint formation rule for arbitrary 1st order formulas. Note that NFP fixpoint logic is an extension of IFP . While IFP formulas can be evaluated in polynomial time, NFP can express PSPACE complete problems, such as the network convergence problem [Fed81]. 5 Actually, it is shown in [AV90] that there is no loss of generality in restricting attention to converging 1st order operators. Noninflationary fixpoint logic was introduced by Abiteboul and Vianu [AV91a] who called it partial fixpoint logic) In particular, they observed that ....

T. Feder. Stable networks and product graphs. PhD thesis, Stanford University, 1981.

....all known polynomially solvable constraint satisfaction problems are simple combinations of the bounded width case and the subgroup case. Remark: A similar situation of only three polynomially solvable cases was observed for Boolean network stability problems by Mayr and Subramanian [35] Feder [12]; the three cases there are monotone networks, linear networks, and nonexpansive networks, in close correspondence with Horn clauses, linear equations modulo 2, and 2SAT respectively; it is the generalization of the nonexpansive case to metric networks that leads to characterizations along the ....

....problem is a constraint satisfaction problem where the template is functional, and where the input structure has the property that every element participates in exactly two relation occurrences, one as an input and one as an output. The input structure is then called a network. The work in [35, 12] established the following. Theorem 15 Every network stability problem over a Boolean functional template is NP complete, with the exception of the following polynomially solvable cases: 0) Functional templates where every relation contains the all zero tuple (or every relation contains the ....

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T. Feder, "Stable Networks and Product Graphs," doctoral dissertation, Stanford University (1991). To appear in Memoirs of the Amer. Math. Soc.

.... network converges, and of finding a stable configuration in a network, are quite simple in the context of sequential computation; they can all be solved in linear time in the scatter free case (a special case, Mayr and Subramanian [5] and in quadratic time in the general nonexpansive case (Feder [1]) An interesting question is the existence of sublinear parallel algorithms with a polynomial number of processors. We present parallel algorithms for the above problems which run in O ( p I) time, with a polynomial number of processors, where I is the size of the input and f(I) O ....

....where m is the total length of the preference lists of individuals. The approach is by means of interior point methods in linear programming. In Sections 2 and 3 we introduce networks of gates and the concepts of nonexpansive and convergent networks. The material in these sections is from Feder [1]. In Section 4 IBM Almaden Research Center, 650 Harry Road, San Jose, CA 95120 y IBM Almaden Research Center, 650 Harry Road, San Jose, California 95120 6099, and School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel. Research supported in part by ONR contracts ....

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T. Feder, Stable Networks and Product Graphs, doctoral dissertation, Stanford University (1991).

.... network converges, and of finding a stable configuration in a network, are quite simple in the context of sequential computation; they can all be solved in linear time in the scatter free case (a special case, Mayr and Subramanian [5] and in quadratic time in the general nonexpansive case (Feder [1]) An interesting question is the existence of sublinear parallel algorithms with a polynomial number of processors. We present parallel algorithms for the above problems which run in O ( p I) time, with a polynomial number of processors, where I is the size of the input and f(I) O ....

....y IBM Almaden Research Center, 650 Harry Road, San Jose, California 95120 6099, and School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel. Research supported in part by ONR contract N00014 91 C 0026. z Department of Computer Science, Stanford University, Stanford, CA 94305 [1]. In Section 4 we study the relation between these concepts and linear programming. In Section 5 we obtain the general result of recognizing stability in a network. This result is then applied to the stable matching problem in Section 6. 2. Gates and Networks A (boolean) assignment is a mapping x ....

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T. Feder, Stable Networks and Product Graphs, doctoral dissertation, Stanford University (1991).

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T. Feder. Stable networks and product graphs. PhD thesis, Stanford University, 1981.

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