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235
Nonholonomic motion planning: Steering using sinusoids
 IEEE fins. Auto. Control
, 1993
"... AbstractIn this paper, we investigate methods for steering systems with nonholonomic constraints between arbitrary configurations. Early work by Brockett derives the optimal controls for a set of canonical systems in which the tangent space to the configuration manifold is spanned by the input vec ..."
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Cited by 251 (15 self)
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AbstractIn this paper, we investigate methods for steering systems with nonholonomic constraints between arbitrary configurations. Early work by Brockett derives the optimal controls for a set of canonical systems in which the tangent space to the configuration manifold is spanned by the input vector fields and their first order Lie brackets. Using Brockett’s result as motivation, we derive suboptimal trajectories for systems which are not in canonical form and consider systems in which it takes more than one level of bracketing to achieve controllability. These trajectories use sinusoids at integrally related frequencies to achieve motion at a given bracketing level. We define a class of systems which can be steered using sinusoids (chained systems) and give conditions under which a class of twoinput systems can be converted into this form. I.
The CRC Handbook Of Combinatorial Designs
, 1995
"... Introduction A group (P; \Delta) is a set P , together with a binary operation \Delta on P , for which 1. an identity element e 2 P exists, i.e. x \Delta e = e \Delta x = e for all x 2 P ; 2. \Delta is associative, i.e. x \Delta (y \Delta z) = (x \Delta y) \Delta z for all x; y; z 2 P ; 3. every el ..."
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Cited by 91 (2 self)
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Introduction A group (P; \Delta) is a set P , together with a binary operation \Delta on P , for which 1. an identity element e 2 P exists, i.e. x \Delta e = e \Delta x = e for all x 2 P ; 2. \Delta is associative, i.e. x \Delta (y \Delta z) = (x \Delta y) \Delta z for all x; y; z 2 P ; 3. every element x 2 P has an inverse, an element x \Gamma1 for which x \Delta x \Gamma1 = x \Gamma1 \Delta<F25.
Solving Difficult Instances of Boolean Satisfiability in the Presence of Symmetry
, 2002
"... Research in algorithms for Boolean satisfiability (SAT) and their implementations [45, 41, 10] has recently outpaced benchmarking efforts. Most of the classic DIMACS benchmarks [21] can now be solved in seconds on commodity PCs. More recent benchmarks [54] take longer to solve due of their large siz ..."
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Cited by 44 (17 self)
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Research in algorithms for Boolean satisfiability (SAT) and their implementations [45, 41, 10] has recently outpaced benchmarking efforts. Most of the classic DIMACS benchmarks [21] can now be solved in seconds on commodity PCs. More recent benchmarks [54] take longer to solve due of their large size, but are still solved in minutes. Yet, small and difficult SAT instances must exist if P##NP. To this end, our work articulates SAT instances that are unusually difficult for their size, including satisfiable instances derived from Very Large Scale Integration (VLSI) routing problems. With an efficient implementation to solve the graph automorphism problem [39, 50, 51], we show that in structured SAT instances difficulty may be associated with large numbers of symmetries.
Symmetry Breaking for Boolean Satisfiability: . . .
"... Boolean Satisfiability solvers improved dramatically over the last seven years [14, 13] and are commonly used in applications such as bounded model checking, planning, and FPGA routing. However, a number of practical SAT instances remain difficult to solve. Recent work pointed out that symmetries i ..."
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Cited by 40 (9 self)
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Boolean Satisfiability solvers improved dramatically over the last seven years [14, 13] and are commonly used in applications such as bounded model checking, planning, and FPGA routing. However, a number of practical SAT instances remain difficult to solve. Recent work pointed out that symmetries in the search space are often to blame [1]. The framework of symmetrybreaking (SBPs) [5], together with further improvements [1], was then used to achieve empirical speedups. For symmetrybreaking to be successful in practice, its overhead must be less than the complexity reduction it brings. In this work we show how logic minimization helps to improve this tradeoff and achieve much better empirical results. We also contribute detailed new studies of SBPs and their efficiency as well as new general constructions of SBPs.
Hurwitz monodromy, spin separation and higher levels of a modular tower
 Proc. Sympos. Pure Math
, 2002
"... D. Fried Abstract. Each finite pperfect group G (p a prime) has a universal central pextension coming from the p part of its Schur multiplier. Serre gave a StiefelWhitney class approach to analyzing spin covers of alternating groups (p = 2) aimed at geometric covering space problems that included ..."
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Cited by 39 (15 self)
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D. Fried Abstract. Each finite pperfect group G (p a prime) has a universal central pextension coming from the p part of its Schur multiplier. Serre gave a StiefelWhitney class approach to analyzing spin covers of alternating groups (p = 2) aimed at geometric covering space problems that included their regular realization for the Inverse Galois Problem. A special case of a general result is that any finite simple group with a nontrivial p part to its Schur multiplier has an infinite string of perfect centerless group covers exhibiting nontrivial Schur multipliers for the prime p. Sequences of moduli spaces of curves attached to G and p, called Modular Towers, capture the geometry of these many appearances of Schur multipliers in degeneration phenomena of HarbaterMumford cover representatives. These are modular curve tower generalizations. So, they inspire conjectures akin to Serre’s open image theorem, including that at suitably high levels we expect no rational points.
New trellis codes based on lattices and cosets
 IEEE Trans. Inform. Theory
, 1987
"... A new technique is proposed for constructing trellis codes, which provides an alternative to Ungerboeck’s method of ‘‘set partitioning’’. The new codes use a signal constellation consisting of points from an ndimensional lattice Λ, with an equal number of points from each coset of a sublattice Λ ′. ..."
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Cited by 37 (7 self)
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A new technique is proposed for constructing trellis codes, which provides an alternative to Ungerboeck’s method of ‘‘set partitioning’’. The new codes use a signal constellation consisting of points from an ndimensional lattice Λ, with an equal number of points from each coset of a sublattice Λ ′. One part of the input stream drives a generalized convolutional code whose outputs are cosets of Λ ′ , while the other part selects points from these cosets. Several of the new codes are better than those previously known.
The Complexity of McKay's Canonical Labeling Algorithm
, 1996
"... We study the time complexity of McKay's algorithm to compute canonical forms and automorphism groups of graphs. The algorithm is based on a type of backtrack search, and it performs pruning by discovered automorphisms and by hashing partial information of vertex labelings. In practice, the algorithm ..."
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Cited by 36 (1 self)
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We study the time complexity of McKay's algorithm to compute canonical forms and automorphism groups of graphs. The algorithm is based on a type of backtrack search, and it performs pruning by discovered automorphisms and by hashing partial information of vertex labelings. In practice, the algorithm is implemented in the nauty package. We obtain colorings of Furer's graphs that allow the algorithm to compute their canonical forms in polynomial time. We then prove an exponential lower bound of the algorithm for connected 3regular graphs of colorclass size 4 using Furer's construction. We conducted experiments with nauty for these graphs. Our experimental results also indicate the same exponential lower bound.
What Do We Know About The Product Replacement Algorithm?
 in: Groups ann Computation III
, 2000
"... . The product replacement algorithm is a commonly used heuristic to generate random group elements in a finite group G, by running a random walk on generating ktuples of G. While experiments showed outstanding performance, until recently there was little theoretical explanation. We give an exten ..."
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Cited by 30 (7 self)
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. The product replacement algorithm is a commonly used heuristic to generate random group elements in a finite group G, by running a random walk on generating ktuples of G. While experiments showed outstanding performance, until recently there was little theoretical explanation. We give an extensive review of both positive and negative theoretical results in the analysis of the algorithm. Introduction In the past few decades the study of groups by means of computations has become a wonderful success story. The whole new field, Computational Group Theory, was developed out of needs to discover and prove new results on finite groups. More recently, the probabilistic method became an important tool for creating faster and better algorithms. A number of applications were developed which assume a fast access to (nearly) uniform group elements. This led to a development of the so called "product replacement algorithm", which is a commonly used heuristic to generate random group elemen...