5,499 research outputs found
Symmetry reduction and heuristic search for error detection in model checking
The state explosion problem is the main limitation of model checking. Symmetries in the system being verified can be exploited in order to avoid this problem by defining an equivalence (symmetry) relation on the states of the system, which induces a semantically equivalent quotient system of smaller size. On the other hand, heuristic search algorithms can be applied to improve the bug finding capabilities of model checking. Such algorithms use
heuristic functions to guide the exploration. Bestfirst
is used for accelerating the search, while A* guarantees optimal error trails if combined with admissible estimates. We analyze some aspects of combining both approaches, concentrating on the problem of finding the optimal path to the equivalence class of a given error state. Experimental
results evaluate our approach
Shimura curve computations via K3 surfaces of Neron-Severi rank at least 19
It is known that K3 surfaces S whose Picard number rho (= rank of the
Neron-Severi group of S) is at least 19 are parametrized by modular curves X,
and these modular curves X include various Shimura modular curves associated
with congruence subgroups of quaternion algebras over Q. In a family of such K3
surfaces, a surface has rho=20 if and only if it corresponds to a CM point on
X. We use this to compute equations for Shimura curves, natural maps between
them, and CM coordinates well beyond what could be done by working with the
curves directly as we did in ``Shimura Curve Computations'' (1998) =
Comment: 16 pages (1 figure drawn with the LaTeX picture environment); To
appear in the proceedings of ANTS-VIII, Banff, May 200
Modular forms and elliptic curves over the cubic field of discriminant -23
Let F be the cubic field of discriminant -23 and let O be its ring of
integers. By explicitly computing cohomology of congruence subgroups of
GL(2,O), we computationally investigate modularity of elliptic curves over F.Comment: Incorporated referee's comment
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