scholarly journals Probabilistic Mathematical Formula Recognition Using a 2D Context-Free Graph Grammar

2011 ◽  
Author(s):  
Mehmet Celik ◽  
Berrin Yanikoglu
Keyword(s):  
Graph Grammar ◽  
Free Graph ◽  
Mathematical Formula ◽  
Mathematical Formula Recognition ◽  
Context Free ◽  
Formula Recognition

scholarly journals Graphs and Decidable Transductions based on Edge Constraints

1994 ◽  
Vol 1 (4) ◽  
Author(s):  
Nils Klarlund ◽  
Michael I. Schwartzbach
Keyword(s):  
Spanning Trees ◽  
Second Order ◽  
Order Logic ◽  
Graph Grammar ◽  
Hoare Logic ◽  
Free Graph ◽  
Graph Families ◽  
Context Free ◽  
Second Order Logic ◽  
Monadic Second Order Logic

We give examples to show that not even <strong> c-edNCE</strong>, the most general known notion of context-free graph grammar, is suited for the specification of some common data structures.<br /> <br />To overcome this problem, we use monadic second-order logic and introduce <em> edge constraints</em> as a new means of specifying a large class of graph families. Our notion stems from a natural dichotomy found in programming practice between ordinary pointers forming spanning trees and auxiliary pointers cutting across.<br /> <br />Our main result is that for certain transformations of graphs definable in monadic second-order logic, the question of whether a graph family given by a specification A is mapped to a family given by a specification B is decidable. Thus a decidable Hoare logic arises.

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