Conditionals: from philosophy to computer science, edited by G. Crocco, L. Fariñas del Cerro, and A. Herzig, Studies in logic and computation, no. 5, Clarendon Press, Oxford University Press, Oxford and New York1995, viii + 368 pp.

1997 ◽  
Vol 62 (4) ◽  
pp. 1487-1490
Author(s):  
Charles B. Cross ◽  
Donald Nute
Keyword(s):  
Computer Science ◽  
Oxford University ◽  
Oxford University Press

Bipartite graphs as polynomials and polynomials as bipartite graphs

2020 ◽  
pp. 2150083
Author(s):  
Andrey Grinblat ◽  
Viktor Lopatkin
Keyword(s):  
Petri Nets ◽  
Computer Science ◽  
Bipartite Graph ◽  
Bipartite Graphs ◽  
Zariski Topology ◽  
Oxford University ◽  
Models Of Concurrency ◽  
Polynomial Formula ◽  
Logic In Computer Science ◽  
Oxford University Press

The aim of this paper is to show that any finite undirected bipartite graph can be considered as a polynomial [Formula: see text], and any directed finite bipartite graph can be considered as a polynomial [Formula: see text], and vise verse. We also show that the multiplication in the semirings [Formula: see text], [Formula: see text] corresponds to an operation of the corresponding graphs. This operation is exactly the product of Petri nets in the sense of Winskel [G. Winskel and M. Nielsen, Models of concurrency, in Handbook of Logic in Computer Science, Vol. 4, eds. Abamsky, Gabbay and Maibaum (Oxford University Press, 1995), pp. 1–148]. As an application, we give an approach to dividing in the semirings [Formula: see text], [Formula: see text], and a criteria for parallalization of Petri nets. Finally, we endow the set of all bipartite graphs with the Zariski topology.

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