32788724
Tight Lower Bounds on the Size of Sweeping Automata
A sweeping automaton is a two-way deterministic finite automaton which makes turns only at the endmarkers. We say that a sweeping automaton is degenerate if the automaton has no left-moving transitions. We show that for each positive integer n, there is a nondeterministic finite automaton An over a two-letter alphabet such that An has n states, whereas the smallest equivalent nondegenerate sweeping automaton has 2n states.
1007735
Structurally Unambiguous Finite Automata
We define a structurally unambiguous finite automaton (SUFA) to be a nondeterministic finite automaton (NFA) with one starting state q0 such that for all input strings w and for any state q, there is at most one path from q0 to q that consumes w. The definition of SUFA differs from the usual definition of an unambiguous finite automaton (UFA) in that the new definition is defined in terms of the transition logic of the finite automaton, and is independent of the choice of final states. We show that SUFA can be exponentially more succinct in the number of states than UFA and MDFA (deterministic finite automata with multiple initial states). Some interesting examples of SUFA are given. We argue that SUFA is a meaningful concept, and can have practical importance as it can implemented efficiently on synchronous models of parallel computation.
33950301
Measuring Nondeterminism in Pushdown Automata
The amount of nondeterminism that a pushdown automaton requires to recognize an input string can be measured by the minimum number of guesses that it must make to accept the string, where guesses are measured in bits of information. When this quantity is unbounded, the rate at which it grows as the length of the string increases serves as a measure of the pushdown automaton's “rate of consumption” of non-determinism. We show that this measure is similar to other complexity measures in that it gives rise to an infinite hierarchy of complexity classes of context-free languages differing in the amount of this resource (nondeterminism) that they require. In addition, we show that there are contextfree languages that can only be recognized by a pushdown automaton whose nondeterminism grows linearly, resolving an open problem in the literature. In particular, {ww R : we {a,b}}*} is such a language.
26148235
On Finite Automata with Limited Nondeterminism
We develop a new algorithm for determining if a given nondeterministic finite automaton is limited in nondeterminism. From this, we show that the number of nondeterministic moves of a finite automaton, if limited, is bounded by 2n−2 where n is the number of states. If the finite automaton is over a one letter alphabet, using Gohon's result the number of nondeterministic moves, if limited, is less than n 2. In both cases, we present families of finite automata demonstrating that the upper bounds obtained are almost tight.
17124839
Separating Exponentially Ambiguous Finite Automata from Polynomially Ambiguous Finite Automata
We resolve an open problem raised by Ravikumar and Ibarra [SIAM J. Comput., 18 (1989), pp. 1263--1282] on the succinctness of representations relating to the types of ambiguity of finite automata. We show that there exists a family of nondeterministic finite automata {An} over a two-letter alphabet such that, for any positive integer n, An is exponentially ambiguous and has n states, whereas the smallest equivalent deterministic finite automaton has 2n states, and any smallest equivalent polynomially ambiguous finite automaton has 2n -1 states.
14116300
A New Perspective of the Proportional Sampling Strategy
To compare the performance of different testing strategies, P-measure and E-measure are two effectiveness measures used in previous analytical studies. P-measure, which is defined as the probability of detecting at least one failure, is a measure of how likely it is that failure-causing inputs are selected at least once as test cases. E-measure, which is defined as the expected number of failures detected, is a measure of how frequently failure-causing inputs are selected as test cases. However, we have noa priori knowledge of how many failure-causing inputs there are, or where they may lie. In this paper, we study P-measure and E-measure in terms of how much attention an arbitrary input receives. In the context of P-measure, the attention received by an arbitrary input is the probability that the input is selected at least once as a test case, while in the context of E-measure, the attention is the expected number of times that an input is selected as a test case. The attentions received by an input using the proportional sampling strategy and random testing are then compared. The attention received by an input is found to be the same under the two testing strategies for E-measure, whereas for P-measure the attention is always higher for the proportional sampling strategy than for random testing. This new perspective allows us to provide simpler proofs of some known results. Furthermore, we are able to show that the difference in the expected number of distinct test cases considered by the proportional sampling strategy is larger than that of random testing by at most 2k, wherek is the number of partitions and is independent of the number of test cases selected.
35807335
Comments on Program Slicing
This correspondence points out some of the problems with Weiser's algorithm [5] for computing program slices. Corrections are made to Weiser's algorithm. It is shown how Weiser's algorithm can be amended to handle loops. Advantages of the Bergeretti and Carre's approach [1] are discussed.
206606389
e-Learning Martial Arts
Traditionally, when people want to learn martial arts, they have to go to training clubs and learn under the coach together with the other students. To reduce the tuition fees, there are usually a lot of students under a single coach and hence, it is difficult for the students to get enough suggestions in the class. It would be far easier if the students could practice themselves at home and ask for suggestions from a virtual coach in the computer. Occasionally, in case they find difficulties going to the next step, they may then approach the real coach for suggestions and training. In this paper, we propose such a training system based on the motion capture system. The system automatically analyzes the motions of the player and gives suggestions. The students can also view the martial art techniques stored in the system or their own techniques captured by the motion capture system from various points of view in order to gain objective ideas of the techniques.
206606372
A Web-Based Chinese Handwriting Education System with Automatic Feedback and Analysis
We propose a web-based Chinese handwriting system that allows students to learn Chinese handwriting at anytime and anywhere. The system combines technologies such as electronic ink, database, Flash animations, and pattern recognition technique to provide students with an intelligent and effective learning environment. In particular, our system contains an Automatic Feedback and Analysis (AFA) tool that can check multiple kinds of handwriting mistakes and provide useful feedback to the user. Survey results show that most users agreed that our proposed system can help them to learn Chinese handwriting more efficiently as well as reducing teachers’ workload. The user evaluation results suggest that it takes less time for users to learn Chinese handwriting with our system than with traditional teaching method.
15674805
Animating reactive motions for biped locomotion
In this paper, we propose a new method for simulating reactive motions for running or walking human figures. The goal is to generate realistic animations of how humans compensate for large external forces and maintain balance while running or walking. We simulate the reactive motions of adjusting the body configuration and altering footfall locations in response to sudden external disturbance forces on the body. With our proposed method, the user first imports captured motion data of a run or walk cycle to use as the primary motion. While executing the primary motion, an external force is applied to the body. The system automatically calculates a reactive motion for the center of mass and angular momentum around the center of mass using an enhanced version of the linear inverted pendulum model. Finally, the trajectories of the generalized coordinates that realize the precalculated trajectories of the center of mass, zero moment point, and angular momentum are obtained using constrained inverse kinematics. The advantage of our method is that it is possible to calculate reactive motions for bipeds that preserve dynamic balance during locomotion, which was difficult using previous techniques. We demonstrate our results on an application that allows a user to interactively apply external perturbations to a running or walking virtual human model. We expect this technique to be useful for human animations in interactive 3D systems such as games, virtual reality, and potentially even the control of actual biped robots.
18767073
Fitting Ellipses to a Region with Application in Calligraphic Stroke Reconstruction
Given a region, it is a challenge to find a set of primitive shapes such as rectangles, circles or ellipses to cover it. This is in fact a set-covering problem, which is known to be NP-hard. The focus of this paper is on fitting a set of ellipses onto an image region. This problem was first formulated by identifying a number of criteria required for the ellipse fitting. A solution is then proposed for automatically determining the set of ellipses that best fits onto an image region. The proposed ellipse fitting algorithm has also been applied to strokes forming characters of Chinese calligraphic artwork. The results show that our proposed algorithm generates ellipses fitting onto stroke regions and capturing the characteristics of the strokes during turning, tilting and back-trace.