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Electronic Colloquium on Computational Complexity

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Reports tagged with dichotomy:
TR96-028 | 9th April 1996
Sanjeev Khanna, Madhu Sudan

The Optimization Complexity of Constraint Satisfaction Problems

In 1978, Schaefer considered a subclass of languages in
NP and proved a ``dichotomy theorem'' for this class. The subclass
considered were problems expressible as ``constraint satisfaction
problems'', and the ``dichotomy theorem'' showed that every language in
this class is either in P, or is NP-hard. This result is in ... more >>>

TR06-094 | 29th July 2006
Parikshit Gopalan, Phokion G. Kolaitis, Elitza Maneva, Christos H. Papadimitriou

The Connectivity of Boolean Satisfiability: Computational and Structural Dichotomies

Revisions: 1

Boolean satisfiability problems are an important benchmark for questions about complexity, algorithms, heuristics and threshold phenomena. Recent work on heuristics, and the satisfiability threshold has centered around the structure and connectivity of the solution space. Motivated by this work, we study structural and connectivity-related properties of the space of solutions ... more >>>

TR07-029 | 20th January 2007
Kazuhisa Makino, Suguru Tamaki, Masaki Yamamoto

A Dichotomy Theorem within Schaefer for the Boolean Connectivity Problem

Revisions: 1

P. Gopalan, P. G. Kolaitis, E. N. Maneva and C. H. Papadimitriou
studied in [Gopalan et al., ICALP2006] connectivity properties of the
solution-space of Boolean formulas, and investigated complexity issues
on connectivity problems in Schaefer's framework [Schaefer, STOC1978].
A set S of logical relations is Schaefer if all relations in ... more >>>

TR09-059 | 2nd July 2009
Gábor Kun, Mario Szegedy


The well known dichotomy conjecture of Feder and
Vardi states that for every finite family Γ of constraints CSP(Γ) is
either polynomially solvable or NP-hard. Bulatov and Jeavons re-
formulated this conjecture in terms of the properties of the algebra
P ol(Γ), where the latter is ... more >>>

TR11-126 | 17th September 2011
Benny Applebaum, Andrej Bogdanov, Alon Rosen

A Dichotomy for Local Small-Bias Generators

We consider pseudorandom generators in which each output bit depends on a constant number of input bits. Such generators have appealingly simple structure: they can be described by a sparse input-output dependency graph and a small predicate that is applied at each output. Following the works of Cryan and Miltersen ... more >>>

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