Efficient program synthesis: Semantics, logic, complexity
The problem of program synthesis is considered.
(1) A computational semantics is introduced for relational knowledge bases. Our semantics naturally arises from practical experience of databases and knowledge bases.
(2) It is stated that the corresponding logic coincides exactly with the intuitionistic one.
(3) Our methods of proof of the general theorems turn out to be very useful for designing new efficient algorithms.
In particular, one can construct a program synthesizer that runs in linear space.
As a corollary, we can explain why there exist programs that solve PSPACE-complete problems “in a reasonable time” despite of their theoretical exponential uniform lower bound.
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