State-feedback implementation of cascade compensators

For general dynamical system Σ and cascade compensator conditions are developed for the existence of a state-feedback law F which when applied to Σ causes the resulting closed-loop system Σ_F to exhibit the same input-output behavior as the cascade connection of Σ with . For a controllable, observable linear system Σ with transfer matrix T_Σ, it is shown that an invertible linear cascade compensator with transfer matrix can be implemented with state feedback if and only if the McMillan degree of T_Σ equal the McMillan degree of .     

Inverse NP Problems

The inverse problem relative to a verifier V of proofs of membership for a NP language is the problem of deciding, given a set π of proofs, whether or not there exists a string x having exactly π as its set of proofs. In this paper, we study the complexity of inverse problems. We develop a new notion of reduction which allows one to compare the complexity of inverse problems. Using this notion, we classify as coNP-complete the inverse problems for the “natural” verifiers of many NP-complete problems. We also show that the inverse complexity of a verifier for a language L cannot be predicted solely from the complexity of L, but rather, is highly dependent upon the choice of verifier used to accept L. In this context, a verifier with a Σ₂ ^p -complete inverse problem is exhibited, giving a new and natural example of a Σ₂ ^p -complete problem.      

A Generalization of AT-Free Graphs and a Generic Algorithm for Solving Triangulation Problems

Abstract. A subset A of the vertices of a graph G is an asteroidal set if for each vertex a ∈ A a connected component of G-N[a] exists containing A\backslash{a} . An asteroidal set of cardinality three is called asteriodal triple and graphs without an asteriodal triple are called AT-free . The maximum cardinality of an asteroidal set of G , denoted by \an(G) , is said to be the asteriodal number of G . We present a scheme for designing algorithms for triangulation problems on graphs. As a consequence, we obtain algorithms to compute graph parameters such as treewidth, minimum fill-in and vertex ranking number. The running time of these algorithms is a polynomial (of degree asteriodal number plus a small constant) in the number of vertices and the number of minimal separators of the input graph.     

Story creation from heterogeneous data sources

There are numerous applications where there is a need to rapidly infer a story about a given subject from a given set of potentially heterogeneous data sources. In this paper, we formally define a story to be a set of facts about a given subject that satisfies a “story length” constraint. An optimal story is a story that maximizes the value of an objective function measuring the goodness of a story. We present algorithms to extract stories from text and other data sources. We also develop an algorithm to compute an optimal story, as well as three heuristic algorithms to rapidly compute a suboptimal story. We run experiments to show that constructing stories can be efficiently performed and that the stories constructed by these heuristic algorithms are high quality stories. We have built a prototype STORY system based on our model—we briefly describe the prototype as well as one application in this paper.

The LabMatrix system

The LabMatrix^™ is a prototyping system designed to give the user a practical and versatile platform for testing microfluidic applications in the fields of health care and life sciences. The LabMatrix^™ system consists of a microfluidic breadboard and cover that align and secure a series of specially designed LabMatrix^™ microfluidic chips. Chips are easily arranged and rearranged into a user-defined fluidic network. The LabMatrix^™ system is designed with maximum flexibility in mind, providing the user with a means to prototype a wide range of microfluidic applications in a short period.     

Compositionally Progressive Solutions of Synchronous FSM Equations

The paper addresses the problem of designing a component that combined with a known part of a system, called the context FSM, is a reduction of a given specification FSM. We study compositionally progressive solutions of synchronous FSM equations. Such solutions, when combined with the context, do not block any input that may occur in the specification, so they are of practical use. We show that, if a synchronous FSM equation has a compositionally progressive solution, then there is a largest regular compositionally progressive solution including all of them. We provide two different algorithms to compute a largest regular compositionally progressive solution: one deletes all compositionally non-progressive strings from a largest solution, the other splits states of a largest solution and then removes those inducing a non-progressive composition.

Verification of schedulability for real-time programs

Assume that a real-time programP ^T consisting of a number of parallel processes is executed on a system having a setPr of processors which are shared between the processes by a real-time schedulerS ^T. Assume that P^T must meet some timing deadlines. We show that such an implementation ofP ^T can be represented as a transformationL(P ^T) and that the deadlines ofP ^T will be met if they are satisfied by the timing properties of the transformed program. The condition for feasibility of a real-time program executed under a scheduler is formalized and rules are provided for verification. The schedulerS ^T can be specifiedgenerically and applied to different programs, making it unnecessary to introduce low-level operations such as scheduling primitives into the programming language. Thus real-time program specification and Schedulability can be considered in the same framework and the timing properties of a program can be determined at the specification level. By separating the specification of the scheduler from that of the program, the feasibility of an implementation can be proved by considering a scheduling policy rather than its implementation details.     

Polynomial time algorithms for computing a representation for minimal unsatisfiable formulas with fixed deficiency

We say a propositional formula F in conjunctive normal form is represented by a formula H and a homomorphism φ, if φ(H)=F. A homomorphism is a mapping consisting of a renaming and an identification of literals. The deficiency of a formula is the difference between the number of clauses and the number of variables. We show that for fixed k?1 and t?1 each minimal unsatisfiable formula with deficiency k can be represented by a formula H with deficiency t and a homomorphism and such a representation can be computed in polynomial time.     

Maximally Concurrent Programs

Typically, program design involves constructing a program P that implements a given specification S; that is, the set ${\overline P}$ of executions of P is a subset of the set ${\overline S}$ of executions satisfying S. In many cases, we seek a program P that not only implements S, but for which ${\overline P}$ = ${\overline S}$. Then, every execution satisfying the specification is a possible execution of the program; we then call P maximal for the specification S. We argue that maximality is an important criterion in the context of designing concurrent programs because it disallows implementations that do not exhibit enough concurrency. In addition, a maximal solution can serve as a basis for deriving a variety of implementations, each appropriate for execution on a specific computing platform. This paper also describes a method for proving the maximality of a program with respect to a given specification. Even though we prove facts about possible executions of programs, there is no need to appeal to branching time logics; we employ a fragment of linear temporal logic for our proofs. The method results in concise proofs of maximality for several non-trivial examples. The method may also serve as a guide in constructing maximal programs. Received September 1997 / Accepted in revised form May 2000     

多项式方程区间内重根的快速判定和裁剪

目的多项式求实根问题有着广泛的应用。改进传统的裁剪方法,在多项式重根的情形下,保持计算稳定性的同时显著地提高相应的收敛阶。方法提出了基于R~3空间内的3次裁剪方法。该方法继承了传统裁剪求根方法的优点,充分利用了Bernstein基函数较好的计算稳定性,同时给出简单方法判别重根的存在性,从而使得重根的情形可以转化为单根的情形。结果与已有的基于R~1和R~2空间的3次裁剪方法相比,本文方法可以具有更好的逼近效果。单根情形下,本文方法与基于R~2空间的3次裁剪方法同时具有5次收敛阶,略高于基于R~1空间3次裁剪方法的4次收敛阶;m(≥2)重根情形下,本文方法理论上可具有5次收敛阶,明显优于已有的基于R~1和R~2空间的3次裁剪方法的4/m或5/m收敛阶。基于R~1,R~2和R~3空间的3次裁剪方法的计算时间复杂度大致相当,均为O(n~2)。结论本文方法可以快速判定重根的情形,同时具有更高的收敛阶和更好的逼近效果。