We derive the first lower bound results on kernel sizes of parameterized problems. The same idea also allows us to sometimes "de-parameterize"
parameterized algorithms.

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We study the notion of "instance compressibility" of NP problems [Harnik-Naor06], closely related to the notion of kernelization in parameterized complexity theory [Downey-Fellows99, Flum-Grohe06, Niedermeier06]. A language $L$ in NP is instance compressible if there
is a polynomial-time computable function $f$ and a set $A$ such that
for each instance ... more >>>

Among others, refining the methods of [Fortnow and Santhanam, ECCC Report TR07-096] we improve a result of this paper and show for any parameterized problem with a ``linear weak OR'' and with NP-hard underlying classical problem that there is no polynomial reduction from the problem to itself that assigns to ... more >>>

Consider the following two-player communication process to decide a language $L$: The first player holds the entire input $x$ but is polynomially bounded; the second player is computationally unbounded but does not know any part of $x$; their goal is to cooperatively decide whether $x$ belongs to $L$ at small ... more >>>