Abstract
The results that we have presented should serve a as a warning: reducing a problem in complexity theory to a communication game may be only a first small step towards the solution, however intuitively clear the game may look like. Still, if we do not look just for record lower bounds, these reductions may often be, in a sense, very rewarding, as they lead to nice mathematical problems and show connections with other branches of mathematics.
An interesting question is, if it is only an accident that we got stuck at difficult combinatorial problems, or if this is due to the fact that the problems are inherently difficult. In the case of the space-time trade-offs it is almost sure that there exists a different, more accessible, way of getting lower bounds. But notice that the problem of proving nonlinear lower bounds on space-time tradeoffs on branching programs is ridiculously weak if compared to real problems such as “P=NP?”. How difficult problems can we expect to encounter when solving those?
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© 1994 Springer-Verlag Berlin Heidelberg
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Pudlák, P. (1994). Unexpected upper bounds on the complexity of some communication games. In: Abiteboul, S., Shamir, E. (eds) Automata, Languages and Programming. ICALP 1994. Lecture Notes in Computer Science, vol 820. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58201-0_53
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DOI: https://doi.org/10.1007/3-540-58201-0_53
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