This paper introduces a midair balloon interface, a fast and soft interactive object in mid-air. Our approach tackles the trade-off between safety and speed by controlling a soft helium-filled balloon with external actuators and sensors. We developed a prototype system that uses airborne ultrasound phased arrays to propel a balloon and high-speed stereo cameras to track its motion. This configuration realizes both a high thrust/weight ratio and such a soft body that is safe-to-collide. We describe a sight-based interaction and a touch-based interaction that leverage the safety and speed of a midair balloon interface. A sight-based interaction allows the user to keep the object inside her/his view within reach by controlling a balloon to follow the direction of the user’s face. A touch-based interaction allows the user to manipulate the object directly with his/her hand, issue a command by moving his/her finger on the surface, and receive vibrotactile feedback produced by vibrating the balloon with amplitude-modulated ultrasound. We describe the implementation and evaluation of the prototype and explore the application scenarios.

The first "natural" languages are established as solvable m deterministic polynomial time, for the recogmtion of which polynomial-time lower bounds can be shown.The k-pebble game problem Is to determine whether the first player has a forced win in the pebble game using only k pebbles.The main result of this paper is that the k-pebble game problem requires ft(n (~-~)/4-') time for its recogmUon on multitape Tunng machines for any ~ > 0. The problem is solvable m deterministic polynomial time.Then we consider other combinatorial game problems that also have nontrivlal polynomial deterministic lower time bounds.

There have been numerous attempts to discuss the time complexity of problems and classify them into hierarchical classes such as P, NP, PSPACE, EXP, etc. A great number of familiar problems have been reported which are complete in NP (nondeterministic polynomial time). Even and Tarjan considered generalized Hex and showed that the problem to determine who wins the game if each player plays perfectly is complete in polynomial space. Shaefer derived some two-person game from NP complete problems which are complete in polynomial space. A rough discussion such as to determine whether or not a given problem belongs to NP is independent of the machine model and the way of defining the size of problems, since any of the commonly used machine models can be simulated by any other with a polynomial loss in running time and by no matter what criteria the size is defined, they differ from each other by polynomial order. However, in precise discussion, for example, in the discussion whether the computation of a problem requires O(n k) time or O(nk+l) time, the complexity heavily depends on machine models and the definition of size of problems. From these points, we introduce somewhat stronger notion of the reducibility.

Since the early 1960's many different models of parallel computation have been developed, some being based on finite state n1achine approaches, others on program schemata models, with many having underlying directed graph representations.[1,2,7,8,10,14,16,17] On the surface these models often appear quite different from one another. Also, the particular types of parallelism problems studied, and the results obtained, seemed often to bear no relation to one another. Thus, the area of modelling parallel computation seemed rather fragmented. In attempts to help unify the area, papers have been written comparing the various models and showing relationships between them. [2.9-13,15] Thus, results obtained in terms of one model often could be translated into results in another model. It is fairly well known by now, for example, that vector addition systems are in some sense "equivalent" to Petri nets,[6,13,16] and that some of the other graphical models for parallel computation are somehow "less powerful" than Petri nets or vector addition systems. This paper presents a comparative study of models of parallel computation using a rather general notion of a homomorphism between computation systems. This notion provides a precise relationship of one computation system being simulated by another computation system. In comparison to previous studies, this approach provides a more precise and deeper understanding of how the properties of the various models are interrelated. Many of the previously discovered relationships follow as corollaries of results obtained here. In particular, the concept of an "isomorphism" between two models turns out to be a particular type of homomorphism which is shown to be both length preserving and bijective. Results in this paper that may be of particular interest include a long list of properties that are preserved under homomorphism, that vector replacement systems can be simulated by vector addition systems, and that generalized Petri nets can be simulated by Petri nets. Here we outline our approach without giving all the precise definitions, and we omit all proofs. A more complete account is given in [9].

A “pebble game” is introduced and some restricted pebble games are considered. It is shown that in each of these games the problem to determine whether there is a winning strategy (two-person game) is harder than the solvability problem (one-person game). We also show that each of these problems is complete in well-known complexity classes. Several familiar games are presented whose winning strategy problems are complete in exponential time.