683638
Descriptional Complexity of Machines with Limited Resources
Over the last 30 years or so many results have appeared on the descriptional complexity of machines with limited resources. Since these results have appeared in a variety of different contexts, our goal here is to provide a survey of these results. Partic- ular emphasis is put on limiting resources (e.g., nondeterminism, ambiguity, lookahead, etc.) for various types of finite state machines, pushdown automata, parsers and cellu- lar automata and on the effect it has on their descriptional complexity. We also address the question of how descriptional complexity might help in the future to solve practical issues, such as software reliability.
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.
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.
15682339
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 nondeterminism. 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 the resource (in this case, nondeterminism) that they require. In addition, we show that there are context-free languages that can only be recognized by a pushdown automaton whose nondeterminism grows linearly, resolving an open problem in the literature. In particular, the set of palindromes is such a language.
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.
39013687
On factorization forests of finite height
Simon (Theoret. Comput. Sci. 72 (1990) 65-94) has proved that every morphism from a free semigroup to a finite semigroup S admits a Ramseyan factorization forest of height at most 9|s|. In this paper, we prove the same result of Simon with an improved bound of 7|S|. We provide a simple algorithm for constructing a factorization forest. In addition, we show that the algorithm cannot be improved significantly. We give examples of semigroup morphism such that any Ramseyan factorization forest for the morphism would require a height not less than |S|.
6994949
Ergodic chaotic parameter modulation with application to digital image watermarking
This paper presents a novel technique for image watermarking based on chaos theory. Chaotic parameter modulation (CPM) is employed to modulate the copyright information into the bifurcating parameter of a chaotic system. The system output is a wideband signal and is used as a watermark to be inserted into the host image. In the detection, a novel method based on the ergodic property of chaotic signal is developed to demodulate the embedded copyright information. Compared to previous works on blind watermarking, the proposed technique can effectively remove the interference from the host image and, thus, improve the detection performance dramatically. Simulation results show that the ergodic CPM approach is effective for image watermarking in terms of noise performance, robustness against attacks, and payload. In addition, its implementation is very simple and the computation speed is fast. Compared to holographic transform domain method and the conventional spread spectrum watermarking scheme, the proposed technique is shown to be superior.
6221143
Analysis of traditional Chinese seals and synthesis of personalized seals
People have long used seals for various purposes. One practical use of seals is for authentication and a lot of research has been focused on this area. In ancient China, seals revealed one's identity and were commonly used by various classes of people. Traditional Chinese seals can also be considered as a form of art, for people to appreciate and to learn about the culture at different dynasties. Nowadays, at this digital age, we would like not only be able to represent the seals in digital format, but also we would like to use image processing techniques to help us better understand them so that although we are not experts we will still be able to produce good designs. In this paper, we propose two things: 1) an analysis method to better understand traditional Chinese seals so that we can describe them in a more semantic way rather than just representing each one as a bitmap image; and 2) a synthesis method to generate a new seal image given a handwritten character, while considering the information obtained from the analysis of the traditional Chinese seals
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.
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.
35321520
Reconstructing the Correct Writing Sequence from a Set of Chinese Character Strokes
A Chinese character is composed of several strokes ordered in a particular sequence. The stroke sequence contains useful online information for handwriting recognition and handwriting education. Although there exist some general heuristic stroke sequence rules, sometimes these rules can be inconsistent making it difficult to apply them to determine the standard writing sequence given a set of strokes. In this paper, we proposed a method to estimate the standard writing sequence given the strokes of a Chinese character. The strokes are modeled as discrete states with the state transition costs determined by the result of the classification into forward/backward order of each stroke pair using the positional features. Candidate sequences are found by shortest path algorithm and the final decision of the stroke sequence is made according to the total handwriting energy in case there is more than one candidate sequence. Experiments show that our results provide better performance than existing approaches.