Boolean satisfiability problem restricted to a planar incidence graph
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Example of a planar SAT problem. The black edges correspond to non-inverted variables and the red edges correspond to inverted variables.
In computer science, the planar 3-satisfiability problem (abbreviated PLANAR 3SAT or PL3SAT) is an extension of the classical Boolean 3-satisfiability problem to a planar incidence graph. In other words, it asks whether the variables of a given Boolean formula—whose incidence graph consisting of variables and clauses can be embedded on a plane—can be consistently replaced by the values TRUE or FALSE in such a way that the formula evaluates to TRUE. If this is the case, the formula is called satisfiable. On the other hand, if no such assignment exists, the function expressed by the formula is FALSE for all possible variable assignments and the formula is unsatisfiable. For example, the formula "a AND NOT b" is satisfiable because one can find the values a = TRUE and b = FALSE, which make (a AND NOT b) = TRUE. In contrast, "a AND NOT a" is unsatisfiable.
Like 3SAT, PLANAR-SAT is NP-complete, and is commonly used in reductions.
NOT b) = TRUE. In contrast, "a AND NOT a" is unsatisfiable. Like 3SAT, PLANAR-SAT is NP-complete, and is commonly used in reductions. Every 3SAT problem...
Satisfiability modulo theories Counting SATPlanarSAT Karloff–Zwick algorithm Circuit satisfiability The SAT problem for arbitrary formulas is NP-complete...
Boolean circuit whose underlying graph is planar) containing only NAND gates with exactly two inputs. Planar Circuit SAT is the decision problem of determining...
classifications) provided in an expository paper by Hubie Chen. Planar TQBF, generalizing PlanarSAT, was proved PSPACE-complete by D. Lichtenstein. M. Garey...
undirected planar graphs of maximum degree three, directed planar graphs with indegree and outdegree at most two, bridgeless undirected planar 3-regular...
points), the problem is NP-hard. This can be proved by reduction from PlanarSAT. For the case in which all holes are single points, several constant-factor...
(DPS) material with negative index material (DNG). It employed a small, planar, negative-refractive-lens interfaced with a positive index, parallel-plate...
reduction. Then, #SAT and #3SAT are counting equivalents, and #3SAT is #P-complete as well. This is the counting version of Planar 3SAT. The hardness...
system is not cartesian because the measurements are angles and are not on a planar surface. A full GCS specification, such as those listed in the EPSG and...
Torres; Schliebner, Ivo; Leister, Dario; Schneitz, Kay (2012). "Regulation of planar growth by the Arabidopsis AGC protein kinase UNICORN". PNAS. 109 (37): 15060–15065...
conjecture: every planar graph can be drawn with integer edge lengths Negami's conjecture on projective-plane embeddings of graphs with planar covers The strong...
In graph theory, a book embedding is a generalization of planar embedding of a graph to embeddings in a book, a collection of half-planes all having the...
compute locations using multilateration. Projected coordinate system (or planar, grid) A standardized cartesian coordinate system that models the Earth...
to practice. In 1980, along with Richard M. Karp, Lipton proved that if SAT can be solved by Boolean circuits with a polynomial number of logic gates...
Kasteleyn, and Neville Temperley, counts the number of perfect matchings in a planar graph in polynomial time. This same task is #P-complete for general graphs...
coordinate system – also called a projected coordinate reference system, planar coordinate system, or grid reference system – is a type of spatial reference...
problem is NP-complete even for planar graphs, this shows that subgraph isomorphism remains NP-complete even in the planar case. Subgraph isomorphism is...
version, in April 1963. The Break, developed by Italian company Pan Auto, sat on a longer wheelbase but was of the same overall length. The model's name...
AAU CubeSat was a CubeSat built and operated by students from Aalborg University in Denmark. AAU CubeSat was launched on 30 June 2003 from the Plesetsk...
may be solved in polynomial time for planar graphs while the independent set problem remains NP-hard on planar graphs. A maximal clique, sometimes called...
{p}{p_{\rm {sat}}}}={\frac {2\gamma V_{\text{m}}}{rRT}},} where p {\displaystyle p} is the actual vapour pressure, p s a t {\displaystyle p_{\rm {sat}}} is...
setting J = j i o n s a t {\displaystyle J=j_{\mathrm {ion} }^{\mathrm {sat} }} : d = 2 3 ( 2 e m i ) 1 / 4 | φ w | 3 / 4 2 π j i o n s a t {\displaystyle...
UTM zone number and hemisphere designator and the easting and northing planar coordinate pair in that zone. The point of origin of each UTM zone is the...
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