LOGCFL
In complexity theory, the complexity class LOGCFL referred to the decision problems which can be reduced with logarithmic memory overhead to a context-free language (English Context -Free Language).
Different characterizations
Apart from the actual definition, there are still some equivalent characterizations of the class LOGCFL:
Auxiliary machinery basement
The decision problems that can solve a nondeterministic auxiliary basement machine with logarithmic work platzbeschränktem tape, a basement storage and polynomially bounded running time. ( Ivan H.Sudborough )
Alternating Turing machines
The decision problems the machines with logarithmic memory overhead and polynomially bounded tree size can be achieved with an Alternating Turing.
Boolean circuits
The decision problems that can be solved by families of "semi- unbounded Boolean circuits" with a limited by O (log n) depth. These circuits consist of AND gates with a limited 2 FanIn and OR gates with arbitrarily large FanIn.
Relation to other complexity classes
From the definition of LOGCFL follows that all languages of LOGCFL can thus be decided in polynomial time LOGCFL ⊆ P. Whether this inclusion is strict, is an important open problem in complexity theory. It is also known that LOGCFL ⊆ NC applies.
Problems in LOGCFL
- Evaluation of acyclic Boolean conjunctive queries
- Homomorphism problem: Is there a homomorphism between two acyclic relational schemes.