Bengt Nordström, Kent Petersson, and Jan M. Smith. Programming in Martin-Löf's type theory. An introduction. The international series of monographs on computer science, no. 7. Clarendon Press, Oxford University Press, Oxford and New York1990, x + 221 pp.

1992 ◽  
Vol 57 (1) ◽  
pp. 272-274
Author(s):  
John C. Mitchell
Keyword(s):  
Computer Science ◽  
Type Theory ◽  
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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