scholarly journals Mechanical theorem proving in projective geometry

1995 ◽  
Vol 13 (1-2) ◽  
pp. 139-172 ◽  
Author(s):  
J�rgen Richter-Gebert
Keyword(s):  
Projective Geometry ◽  
Theorem Proving ◽  
Mechanical Theorem Proving ◽  
Mechanical Theorem

scholarly journals Subtree matching by pushdown automata

2010 ◽  
Vol 7 (2) ◽  
pp. 331-357 ◽  
Author(s):  
Tomás Flouri ◽  
Jan Janousek ◽  
Bořivoj Melichar
Keyword(s):  
Programming Languages ◽  
Theorem Proving ◽  
Systematic Approach ◽  
Finite Automata ◽  
Term Rewriting ◽  
Mechanical Theorem Proving ◽  
Pushdown Automaton ◽  
String Pattern ◽  
Pushdown Automata ◽  
Mechanical Theorem

Subtree matching is an important problem in Computer Science on which a number of tasks, such as mechanical theorem proving, term-rewriting, symbolic computation and nonprocedural programming languages are based on. A systematic approach to the construction of subtree pattern matchers by deterministic pushdown automata, which read subject trees in prefix and postfix notation, is presented. The method is analogous to the construction of string pattern matchers: for a given pattern, a nondeterministic pushdown automaton is created and is then determinised. In addition, it is shown that the size of the resulting deterministic pushdown automata directly corresponds to the size of the existing string pattern matchers based on finite automata.

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