This paper considers the problem of planning collision-free motion of three disks in the plane. One of the three disks, the robot, can autonomously translate in the plane, the other two move only when in contact with the robot. This represents the abstract formulation of a manipulation planning problem. Despite the simplicity of the formulation, the decidability of the problem had remained unpr...

We develop an analogue of the Birman exact sequence for the Torelli subgroup of AutpFnq. This builds on earlier work of the authors who studied an analogue of the Birman exact sequence for the entire group AutpFnq. These results play an important role in the authors’ recent work on the second homology group of the Torelli group.

In this paper we introduce a novel use of the lexicographic semiring and motivate its use for speech and language processing tasks. We prove that the semiring allows for exact encoding of backoff models with epsilon transitions. This allows for off-line optimization of exact models represented as large weighted finite-state transducers in contrast to implicit (on-line) failure transition repres...

A chain complex (or simply a complex ) C∗ is a family of R-modules Cn, n ∈ Z, along with R-homomorphisms dn : Cn → Cn−1 called differentials, satisfying dndn+1 = 0 for all n. A chain complex with only finitely many Cn’s is allowed; it can always be extended with the aid of zero modules and zero maps. [In topology, Cn is the abelian group of nchains, that is, all formal linear combinations with ...