Semi-stable models of modular curves X0(p2) and some arithmetic applications

Many efficient algorithms for the computation of optimum stable models in the context of Answer Set Programming (ASP) are based on unsatisfiable core analysis. Among them, algorithm OLL was the first introduced in the context of ASP, whereas algorithms ONE and PMRES were first introduced for solving the Maximum Satisfiability problem (MaxSAT) and later on adapted to ASP. In this paper, we present the porting to ASP of another state-of-the-art algorithm introduced for MaxSAT, namely K, which generalizes ONE and PMRES. Moreover, we present a new algorithm called OLL-IN-ONE that compactly encodes all aggregates of OLL by taking advantage of shared aggregate sets propagators. The performance of the algorithms have been empirically compared on instances taken from the latest ASP Competition.

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Normalizers of non-split Cartan subgroups, modular curves, and the class number one problem

Journal of Number Theory ◽

10.1016/j.jnt.2010.06.005 ◽

2010 ◽

Vol 130 (12) ◽

pp. 2753-2772 ◽

Cited By ~ 11

Author(s):

Burcu Baran

Keyword(s):

Class Number ◽

Modular Curves ◽

Cartan Subgroups

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The interpretation of unsolvable λ-terms in models of untyped λ-calculus

Journal of Symbolic Logic ◽

10.2307/2586665 ◽

1998 ◽

Vol 63 (4) ◽

pp. 1529-1548 ◽

Cited By ~ 4

Author(s):

Rainer Kerth

Keyword(s):

Graph Model ◽

Stable Model ◽

Graph Models ◽

Stable Models

AbstractOur goal in this paper is to analyze the interpretation of arbitrary unsolvable λ-terms in a given model of λ-calculus. We focus on graph models and (a special type of) stable models. We introduce the syntactical notion of a decoration and the semantical notion of a critical sequence. We conjecture that any unsolvable term β-reduces to a term admitting a decoration. The main result of this paper concerns the interconnection between those two notions: given a graph model or stable model , we show that any unsolvable term admitting a decoration and having a non-empty interpretation in generates a critical sequence in the model.In the last section, we examine three classical graph models, namely the model of Plotkin and Scott, Engeler's model and Park's model . We show that and do not contain critical sequences whereas does.

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On the genus of some modular curves of level N

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972700017755 ◽

1996 ◽

Vol 54 (2) ◽

pp. 291-297 ◽

Cited By ~ 10

Author(s):

Chang Heon Kim ◽

Ja Kyung Koo

Keyword(s):

Modular Curves

We estimate the genus of the modular curves X1(N).

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Zeta functions of twisted modular curves

Journal of the Australian Mathematical Society ◽

10.1017/s144678870001140x ◽

2006 ◽

Vol 80 (1) ◽

pp. 89-103 ◽

Cited By ~ 1

Author(s):

Cristian Virdol

Keyword(s):

Zeta Function ◽

Galois Group ◽

Complex Plane ◽

Zeta Functions ◽

Modular Curves ◽

Absolute Galois Group ◽

Modular Curve ◽

The Absolute

AbstractIn this paper we compute and continue meromorphically to the whole complex plane the zeta function for twisted modular curves. The twist of the modular curve is done by a modprepresentation of the absolute Galois group.

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