15577452
New Complexity Results for Some Linear Counting Problems Using Minimal Solutions to Linear Diophantine Equations
The linear reachability problem is to decide whether there is an execution path in a given finite state transition system such that the counts of labels on the path satisfy a given linear constraint. Using results on minimal solutions (in nonnegative integers) for linear Diophantine systems, we obtain new complexity results for the problem, as well as for other linear counting problems of finite state transition systems and timed automata. In contrast to previously known results, the complexity bounds obtained in this paper are polynomial in the size of the transition system in consideration, when the linear constraint is fixed.
342925
Signaling P Systems and Verification Problems
We introduce a new model of membrane computing system (or P system), called signaling P system. It turns out that signaling systems are a form of P systems with promoters that have been studied earlier in the literature. However, unlike non-cooperative P systems with promoters, which are known to be universal, non-cooperative signaling systems have decidable reachability properties. Our focus in this paper is on verification problems of signaling systems; i.e., algorithmic solutions to a verification query on whether a given signaling system satisfies some desired behavioral property. Such solutions not only help us understand the power of “maximal parallelism” in P systems but also would provide a way to validate a (signaling) P system in vitro through digital computers when the P system is intended to simulate living cells. We present decidable and undecidable properties of the model of non-cooperative signaling systems using proof techniques that we believe are new in the P system area. For the positive results, we use a form of “upper-closed sets” to serve as a symbolic representation for configuration sets of the system, and prove decidable symbolic model-checking properties about them using backward reachability analysis. For the negative results, we use a reduction via the undecidability of Hilbert’s Tenth Problem. This is in contrast to previous proofs of universality in P systems where almost always the reduction is via matrix grammar with appearance checking or through Minsky’s two-counter machines. Here, we employ a new tool using Diophantine equations, which facilitates elegant proofs of the undecidable results. With multiplication being easily implemented under maximal parallelism, we feel that our new technique is of interest in its own right and might find additional applications in P systems.
14050589
Testability of Oracle Automata
An oracle finite automaton (OFA) is a finite/Buchi automaton augmented with a finite number of unbounded, one-way, and writable query tapes. By each transition, an OFA can read an input symbol, append a symbol to the end of a query tape, erase the content of a query tape, or query an oracle with the content of a query tape (called a query string). Here, an oracleO is a language in some language class $\mathcal{O}$ (all oracles in the OFA must be in the same language class $\mathcal{O}$, and we denote such OFAs with OFA$^\mathcal{O}$. The name of “oracle” comes from the fact that, except for its language class, the definition of O is not given. However, the oracle O can always be queried with the answer whether a query string w is in O.
29028846
Reuse or Never Reuse the Deleted Labels in XML Query Processing Based on Labeling Schemes
To facilitate the XML query processing, several kinds of labeling schemes have been proposed. Based on the labeling schemes, the ancestor-descendant and parent-child relationships in XML queries can be quickly determined without accessing the original XML file. Recently, more researches are focused on how to update the labels when nodes are inserted into the XML. However how to process the deleted labels are not discussed previously. We think that the deleted labels can be processed in two different directions: (1) reuse all the deleted labels to control the label size increasing speed and improve the query performance; (2) never reuse the deleted labels to query different versions of the XML data based on labeling schemes. In this paper, we firstly introduce our previous work, called QED, which can completely avoid the re-labeling in XML updates. Secondly based on QED we propose a new algorithm, called Reuse, which can reuse all the deleted labels to control the label size increasing speed; meanwhile the Reuse algorithm can completely avoid the re-labeling also. Thirdly to query different versions of the XML data, we propose another new algorithm, called NeverReuse, which is the only approach that never reuses any deleted labels. Extensive experimental results show that the algorithms proposed in this paper can control the label size increasing speed when reusing all the deleted labels, and is the only approach to query different versions of the XML data based on labeling schemes.
17566608
Porosity of mutually nearest and mutually furthest points in Banach spaces
Let X be a real strictly convex and Kadec Banach space and G a nonempty closed relatively boundedly weakly compact subset of X. Let B(X) (resp. K(X)) be the family of nonempty bounded closed (resp. compact) subsets of X endowed with the Hausdorff distance and let BG(X) denote the closure of the set {A ∈ B(X) : A ∩ G = φ} and KG(X) = BG(X)∩K(X). We introduce the admissible family A of B(X) and prove that EAo(G) (resp. EoA(G)), the set of all subsets F ∈ A ⊆ BG(X) (resp. F ∈ A ⊆ BG(X)) such that the minimization problem min(F, G) (resp. the maximization problem max(F, G)) is well-posed, is a dense Gδ-subset of A. Furthermore, when X is uniformly convex, we prove that A\EAo(G) and A\EoA(G) are σ-porous in A.
35216739
Image Smoothing Using Parametric Relaxation
Abstract A new image-smoothing algorithm which smooths the image while preserving discontinuities is developed. The method poses the smoothing problem as an estimation problem of the maximum a posteriori probability of a pixel having a certain gray level. A prior probability density function is assigned to each pixel from the raw data, which is an estimate of the gray-level uncertainty. The algorithm is an application of the random measure field in image processing. Contextual information from neighbors is used in refining the probability distribution of each pixel, which is a continuous version of the relaxation algorithm. The way of parametrizing the probability functions enables the derivation of an efficient iterative formula for updating the gray-level values.
218270
Cryptanalysis of a multistage encryption system
This paper analyzes the security of a new multistage encryption system (MES) recently proposed in ISCAS'2004. It is found that MES is insecure against a differential chosen-plaintext/ciphertext attack. Experiments are given to support the proposed attack. It is also pointed out that the security of MES against brute-force attacks is not sufficiently high.
7000090
On isomorphisms of finite Cayley graphs--a survey
The isomorphism problem for Cayley graphs has been extensively investigated over the past 30 years. Recently, substantial progress has been made on the study of this problem, many long-standing open problems have been solved, and many new research problems have arisen. The results obtained, and methods developed in this area have also effectively been used to solve other problems regarding finite vertex-transitive graphs. The methods used in this area range from deep group theory, including the finite simple group classification, through to combinatorial techniques. This article is devoted to surveying results, open problems and methods in this area.