Ernst W. Mayr

Bio: Ernst W. Mayr is an academic researcher from Technische Universität München. The author has contributed to research in topics: Parallel algorithm & Hypercube. The author has an hindex of 23, co-authored 92 publications receiving 2236 citations. Previous affiliations of Ernst W. Mayr include Goethe University Frankfurt & Stanford University.

An Algorithm for the General Petri Net Reachability Problem

Abstract: An algorithm is presented for the general Petri net reachability problem. It is based on a generalization of the basic reachability tree construction which is made symmetric with respect to the ini...

An algorithm for the general Petri net reachability problem

Abstract: An algorithm is presented for the general Petri net reachability problem based on a generalization of the basic reachability construction which is symmetric with respect to the initial and final marking. Sets of transition sequences described by finite automata are used for approximations to firing sequences, and the approximation error is assessed by uniformly constructable Presburger expressions. The approximation algorithm is iterated until a sufficient criterion for reachability can be given, not-withstanding the remaining uncertainty.

Persistence of vector replacement systems is decidable

Abstract: In a persistent vector replacement system (VRS) or Petri net, an enabled transition can become disabled only by firing itself. Here, an algorithm is presented which allows to decide whether an arbitrary VRS is persistent or not, and if so, to construct a semilinear representation of the set of states reachable in the system.

I and i

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

Petri nets: Properties, analysis and applications

Abstract: Starts with a brief review of the history and the application areas considered in the literature. The author then proceeds with introductory modeling examples, behavioral and structural properties, three methods of analysis, subclasses of Petri nets and their analysis. In particular, one section is devoted to marked graphs, the concurrent system model most amenable to analysis. Introductory discussions on stochastic nets with their application to performance modeling, and on high-level nets with their application to logic programming, are provided. Also included are recent results on reachability criteria. Suggestions are provided for further reading on many subject areas of Petri nets. >

Algorithms in real algebraic geometry

Abstract: Algebraically Closed Fields- Real Closed Fields- Semi-Algebraic Sets- Algebra- Decomposition of Semi-Algebraic Sets- Elements of Topology- Quantitative Semi-algebraic Geometry- Complexity of Basic Algorithms- Cauchy Index and Applications- Real Roots- Cylindrical Decomposition Algorithm- Polynomial System Solving- Existential Theory of the Reals- Quantifier Elimination- Computing Roadmaps and Connected Components of Algebraic Sets- Computing Roadmaps and Connected Components of Semi-algebraic Sets

The Computational Structure of Monotone Monadic SNP and Constraint Satisfaction: A Study through Datalog and Group Theory

Abstract: This paper starts with the project of finding a large subclass of NP which exhibits a dichotomy. The approach is to find this subclass via syntactic prescriptions. While the paper does not achieve this goal, it does isolate a class (of problems specified by) "monotone monadic SNP without inequality" which may exhibit this dichotomy. We justify the placing of all these restrictions by showing, essentially using Ladner's theorem, that classes obtained by using only two of the above three restrictions do not show this dichotomy. We then explore the structure of this class. We show that all problems in this class reduce to the seemingly simpler class CSP. We divide CSP into subclasses and try to unify the collection of all known polytime algorithms for CSP problems and extract properties that make CSP problems NP-hard. This is where the second part of the title, "a study through Datalog and group theory," comes in. We present conjectures about this class which would end in showing the dichotomy.