1397724
Descriptional complexity of nfa of different ambiguity
In this paper, we study the tradeoffs in descriptional complexity of NFA (nondeterministic finite automata) of various amounts of ambiguity. We say that two classes of NFA are separated if one class can be exponentially more succinct in descriptional sizes than the other. New results are given for separating DFA (deterministic finite automata) from UFA (unambiguous finite automata), UFA from MDFA (DFA with multiple initial states) and UFA from FNA (finitely ambiguous NFA). We present a family of regular languages that we conjecture to be a good candidate for separating FNA from LNA (linearly ambiguous NFA).
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.
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.
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.
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.
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.
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.
16283263
Robust classification of blurred imagery
In this paper, we present two novel approaches for the classification of blurry images. It is assumed that the blur is linear and space invariant, but that the exact blurring function is unknown. The proposed fusion-based approaches attempt to perform the simultaneous tasks of blind image restoration and classification. We call such a problem blind image fusion. The techniques are implemented using the nonnegativity and support constraints recursive inverse filtering (NAS-RIF) algorithm for blind image restoration and the Markov random field (RIRF)-based fusion method for classification by Schistad-Solberg et al. Simulation results on synthetic and real photographic data demonstrate the potential of the approaches. The algorithms are compared with one another and to situations in which blind blur removal is not attempted.
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.
30262171
Improving defect removal effectiveness for software development
The paper first reviews the industry statistics on defects, presents a model of defect removal, then develops the relationships between the defect removal effectiveness of different defect removal phases. The defect removal effectiveness of an average organization is determined based on published data. Combining the industry data with the defect removal model, insights into improvement of the defect removal process can be gained. It is determined that the defect removal effectiveness of individual phases cannot be higher than that of the overall development process. Also, introducing inspection to the software development process will certainly allow an average organization to achieve higher defect removal effectiveness.