# The Nondeterministic Constraint Logic Model of Computation: Reductions and Applications

@inproceedings{Hearn2002TheNC,
title={The Nondeterministic Constraint Logic Model of Computation: Reductions and Applications},
author={Robert A. Hearn and Erik D. Demaine},
booktitle={ICALP},
year={2002}
}
• Published in ICALP 4 May 2002
• Computer Science
We present a nondeterministic model of computation based on reversing edge directions in weighted directed graphs with minimum in-flow constraints on vertices. Deciding whether this simple graph model can be manipulated in order to reverse the direction of a particular edge is shown to be PSPACE-complete by a reduction from Quantified Boolean Formulas. We prove this result in a variety of special cases including planar graphs and highly restrictedv ertex configurations, some of which correspond…
28 Citations
Parameterized Complexity of Graph Constraint Logic
It is shown that reconfiguration versions of several classical graph problems are PSPACE-complete on planar graphs of bounded bandwidth and that Rush Hour, generalized to $k\times n$ boards, is PSPace-complete even when $k$ is at most a constant.
284 Parameterized Complexity of Graph Constraint Logic
It is shown that reconfiguration versions of several classical graph problems are PSPace-complete on planar graphs of bounded bandwidth and that Rush Hour, generalized to k × n boards, is PSPACE-complete even when k is at most a constant.
Constraint Logic: A Uniform Framework for Modeling Computation as Games
• Computer Science
2008 23rd Annual IEEE Conference on Computational Complexity
• 2008
A simple game family, called constraint logic, where players reverse edges in a directed graph while satisfying vertex in-flow constraints is introduced, which makes it substantially easier to prove completeness of such games in their appropriate complexity classes.
Push-2-f is pspace-complete
• Mathematics
CCCG
• 2002
It is proved that Push-k-F and Push-*-F are PSPACEcomplete for k ≥ 2 using a reduction from Nondeterministic Constraint Logic (NCL) [8].
Games, puzzles and computation
• Philosophy
• 2006
This thesis develops the idea of game as computation to a greater degree than has been done previously, and presents a general family of games, called Constraint Logic, which is both mathematically simple and ideally suited for reductions to many actual board games.
The Connectivity of Boolean Satisfiability: Computational and Structural Dichotomies
• Mathematics
SIAM J. Comput.
• 2009
The results assert that the intractable side of the computational dichotomies is PSPACE-complete, while the tractable side—which includes but is not limited to all problems with polynomial-time algorithms for satisfiability—is in P for the $st$-connectivity question, and in coNP for the connectivity question.
Connectivity of Boolean satisfiability
A computational dichotomy is proved for the st-connectivity problem, asserting that it is either solvable in polynomial time or PSPACE-complete, and an aligned structural dichotomy for the connectivity problem is proved, asserting the maximal diameter of connected components is either linear in the number of variables, or can be exponential.
Limits of Rush Hour Logic Complexity
• Computer Science
ArXiv
• 2005
The authors show how the Rush Hour model supports polynomial space computation, using certain car configurations as building blocks to construct boolean circuits for a cpu and memory.
Belief propagation algorithms for constraint satisfaction problems
• Computer Science
• 2006
This thesis shows that survey propagation, which is the most effective heuristic for random 3-SAT problems with density of clauses close to the conjectured satisfiability threshold, is in fact a belief propagation algorithm, and defines a parameterized distribution on partial assignments, and shows that applying belief propagation to this distribution recovers a known family of algorithms.
Reconfiguring Undirected Paths
• Mathematics, Computer Science
• 2019
We consider problems in which a simple path of fixed length, in an undirected graph, is to be shifted from a start position to a goal position by moves that add an edge to either end of the path and

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