In a seminal paper from 1985, Sistla and Clarke showed
that the model-checking problem for Linear Temporal Logic (LTL) is either NP-complete
or PSPACE-complete, depending on the set of temporal operators used.
If, in contrast, the set of propositional operators is restricted, the complexity may decrease.
... more >>>

The Hartmanis--Immerman--Sewelson theorem is the classical link between the exponential and the polynomial time realm. It states that NE = E if, and only if, every sparse set in NP lies in P. We establish similar links for classes other than sparse sets:

1. E = UE if, and only ... more >>>

Most state-of-the-art satisfiability algorithms today are variants of
the DPLL procedure augmented with clause learning. The main bottleneck
for such algorithms, other than the obvious one of time, is the amount
of memory used. In the field of proof complexity, the resources of
time and memory correspond to the length ... more >>>