649 research outputs found
Bounded Context Switching for Valence Systems
We study valence systems, finite-control programs over infinite-state memories modeled in terms of graph monoids. Our contribution is a notion of bounded context switching (BCS). Valence systems generalize pushdowns, concurrent pushdowns, and Petri nets. In these settings, our definition conservatively generalizes existing notions. The main finding is that reachability within a bounded number of context switches is in NPTIME, independent of the memory (the graph monoid). Our proof is genuinely algebraic, and therefore contributes a new way to think about BCS. In addition, we exhibit a class of storage mechanisms for which BCS reachability belongs to PTIME
Normaliz: Algorithms for Affine Monoids and Rational Cones
Normaliz is a program for solving linear systems of inequalities. In this
paper we present the algorithms implemented in the program, starting with
version 2.0
Challenging computations of Hilbert bases of cones associated with algebraic statistics
In this paper we present two independent computational proofs that the monoid
derived from contingency tables is normal, completing the
classification by Hibi and Ohsugi. We show that Vlach's vector disproving
normality for the monoid derived from contingency tables is
the unique minimal such vector up to symmetry. Finally, we compute the full
Hilbert basis of the cone associated with the non-normal monoid of the
semi-graphoid for . The computations are based on extensions of the
packages LattE-4ti2 and Normaliz.Comment: 10 page
Formalized proof, computation, and the construction problem in algebraic geometry
An informal discussion of how the construction problem in algebraic geometry
motivates the search for formal proof methods. Also includes a brief discussion
of my own progress up to now, which concerns the formalization of category
theory within a ZFC-like environment
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