Program slicing is a method for automatically decomposing programs by analyzing their data flow and control flow. Starting from a subset of a program's behavior, slicing reduces that program to a minimal form which still produces that behavior. The reduced program, called a ``slice,'' is an independent program guaranteed to represent faithfully the original program within the domain of the specified subset of behavior. Some properties of slices are presented. In particular, finding statement-minimal slices is in general unsolvable, but using data flow analysis is sufficient to find approximate slices. Potential applications include automatic slicing tools for debuggng and parallel processing of slices.

Program Slicing

PART I: FOUNDATIONS 1. Introduction to Fixed-Parameter Algorithms 2. Preliminaries and Agreements 3. Parameterized Complexity Theory - A Primer 4. Vertex Cover - An Illustrative Example 5. The Art of Problem Parameterization 6. Summary and Concluding Remarks PART II: ALGORITHMIC METHODS 7. Data Reduction and Problem Kernels 8. Depth-Bounded Search Trees 9. Dynamic Programming 10. Tree Decompositions of Graphs 11. Further Advanced Techniques 12. Summary and Concluding Remarks PART III: SOME THEORY, SOME CASE STUDIES 13. Parameterized Complexity Theory 14. Connections to Approximation Algorithms 15. Selected Case Studies 16. Zukunftsmusik References Index

Invitation to fixed-parameter algorithms

A code clone is a code portion in source files that is identical or similar to another. Since code clones are believed to reduce the maintainability of software, several code clone detection techniques and tools have been proposed. This paper proposes a new clone detection technique, which consists of the transformation of input source text and a token-by-token comparison. For its implementation with several useful optimization techniques, we have developed a tool, named CCFinder (Code Clone Finder), which extracts code clones in C, C++, Java, COBOL and other source files. In addition, metrics for the code clones have been developed. In order to evaluate the usefulness of CCFinder and metrics, we conducted several case studies where we applied the new tool to the source code of JDK, FreeBSD, NetBSD, Linux, and many other systems. As a result, CCFinder has effectively found clones and the metrics have been able to effectively identify the characteristics of the systems. In addition, we have compared the proposed technique with other clone detection techniques.

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CCFinder: a multilinguistic token-based code clone detection system for large scale source code

This comprehensive textbook presents a clean and coherent account of most fundamental tools and techniques in Parameterized Algorithms and is a self-contained guide to the area. The book covers many of the recent developments of the field, including application of important separators, branching based on linear programming, Cut & Count to obtain faster algorithms on tree decompositions, algorithms based on representative families of matroids, and use of the Strong Exponential Time Hypothesis. A number of older results are revisited and explained in a modern and didactic way. The book provides a toolbox of algorithmic techniques. Part I is an overview of basic techniques, each chapter discussing a certain algorithmic paradigm. The material covered in this part can be used for an introductory course on fixed-parameter tractability. Part II discusses more advanced and specialized algorithmic ideas, bringing the reader to the cutting edge of current research. Part III presents complexity results and lower bounds, giving negative evidence by way of W[1]-hardness, the Exponential Time Hypothesis, and kernelization lower bounds. All the results and concepts are introduced at a level accessible to graduate students and advanced undergraduate students. Every chapter is accompanied by exercises, many with hints, while the bibliographic notes point to original publications and related work.

Parameterized Algorithms

CONTENTS 7 Acknowledgments Many people gave substantial suggestions to improve the contents of this book. These are, in alphabetic order, Introduction During the past few years, several of us have been asked many times about references on finite tree automata. On one hand, this is the witness of the liveness of this field. On the other hand, it was difficult to answer. Besides several excellent survey chapters on more specific topics, there is only one monograph devoted to tree automata by Gécseg and Steinby. Unfortunately, it is now impossible to find a copy of it and a lot of work has been done on tree automata since the publication of this book. Actually using tree automata has proved to be a powerful approach to simplify and extend previously known results, and also to find new results. For instance recent works use tree automata for application in abstract interpretation using set constraints, rewriting, automated theorem proving and program verification, databases and XML schema languages. Tree automata have been designed a long time ago in the context of circuit verification. Many famous researchers contributed to this school which was headed by A. Church in the late 50's and the early 60's: B. Trakhtenbrot, Many new ideas came out of this program. For instance the connections between automata and logic. Tree automata also appeared first in this framework, following the work of Doner, Thatcher and Wright. In the 70's many new results were established concerning tree automata, which lose a bit their connections with the applications and were studied for their own. In particular, a problem was the very high complexity of decision procedures for the monadic second order logic. Applications of tree automata to program verification revived in the 80's, after the relative failure of automated deduction in this field. It is possible to verify temporal logic formulas (which are particular Monadic Second Order Formulas) on simpler (small) programs. Automata, and in particular tree automata, also appeared as an approximation of programs on which fully automated tools can be used. New results were obtained connecting properties of programs or type systems or rewrite systems with automata. Our goal is to fill in the existing gap and to provide a textbook which presents the basics of tree automata and several variants of tree automata which have been devised for applications in the aforementioned domains. We shall discuss only finite tree automata, and the …

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Tree Automata Techniques and Applications

We study grasps by a robot hand with three spring-loaded fingers. In two dimensions, the hand can grasp any polygon stably. That is, the grip is at a local minimum of the potential energy function defined by the springs of the fingers, ignoring friction. Surprisingly, under some conditions an equilibrium grasp on a circle is unstable even with respect to translation. In three dimensions, the hand can grasp and lift any cylindrical surface with a polygonal cross-section. In contrast we show that a hand with finger angles fixed at 120°, as proposed by Hanafusa and Asada, generally can not achieve a two-dimensional stable grip in the absence of friction.

Stable prehension with a multi-fingered hand

ABSTRACf This paper describes a general technique that can be used to obtain approximation algorithms for various NP-complete problems on planar graphs. The strategy depends on decom­ posing a planar graph into subgraphs of a form we call k­ outerplanar. For fixed k, the problems of interest are solv­ able optimally in linear time on k -outerplanar graphs by dynamic programming. For general planar graphs, if the problem is a maximization problem, such as maximum in­ dependent set, this technique gives for each k a linear time algorithm that produces a solution whose size is at least (k -1)/k optimal. If the problem is a minimization problem, such as minimum vertex cover, it gives for each k a linear time algorithm that produces a solution whose size is at most (k+l)/k optimal. Taking k-cloglogn or k-clogn, where n is the number of nodes and c is some constant, we get po­ lynomial time approximation schemes, i.e. algorithms whose solution sizes converge toward optimal as n increases. The class of problems for which this approach provides approxi­ mation schemes includes maximum independent set, max­ imum tile salvage, partition into triangles, maximum H­ matching, minimum vertex cover, minimum dominating set, and minimum edge dominating set. For these and certain other problems, the proof of solvability on k -outerplanar graphs also enlarges the class of planar graphs for which the problems are known to be solvable.

Approximation Algorithms for NP.Complete Problems on Planar Graphs (Preliminary Version

Interest in the study of sets of trees, tree languages, has led to the definition of finite automata which accept trees [2,11] and transducers which map trees into other trees [7,9,10]. These generalized machines may read treesfinite automata which accept trees [2,11] and of transducers which map trees into other trees [7,9,10]. These generalized machines may read trees either “top-down” (from the root toward the leaves) or “bottom-up” (from the leaves toward the root). Here it is shown that both the class of top-down transductions and the class of bottom-up transductions can be characterized in terms of two restricted classes of tree transductions. From these ductions and the class of bottom-up transductions can be characterized in terms of two restricted classes of tree transductions. From these characterizations, it is shown that the composition of any n bottom-up transductions can be realized by the composition of n+1 top-down transductions, and similarly, the composition of any n top-down transductions can be realized by the composition of n+1 bottom-up transductions. Next, we study the families of tree languages which can be obtained from the recognizable sets (sets accepted by finite tree automata) by the composition of n top-down or bottom-up transductions, n>0. The yield operation, which concatenates the leaves of a tree from left to right to form a of string, languages from the hierarchy of families of tree languages. It is shown that each family of string languages in this hierarchy is properly contained in the family of context-sensitive languages.

Tree transductions and families of tree languages

When trees are denoted by “terms” or “parenthesized expressions”, which are strings, the class of top-down tree transducers (automata which map trees into trees and read their input trees from the root toward the leaves) form a subclass of a nondeterministic version of the generalized syntax directed translations of Aho and Ullman. It is shown that every nondeterministic syntax directed translation (NGSDT), and therefore every top-down tree transduction, can be carried out by a Turing machine which uses an amount of work space which is linear with respect to the size of the input and output. For every n, the family consisting of the images of recognizable sets of trees under the composition of n top-down transductions is shown to be properly contained in the family of deterministic context-sensitive languages.

Generalized Syntax Directed Translation, Tree Transducers, and Linear Space

Tree transducers (automata which read finite labeled trees and output finite labeled trees) are used to define a hierarchy of families of “tree languages” (sets of trees). In this hierarchy, families generated by “top-down” tree transducers (which read trees from the root toward the leaves) alternate with families generated by “bottom-up” tree transducers (which read trees from the leaves toward the root). A hierarchy of families of string languages is obtained from the first hierarchy by the “yield” operation (concatenating the labels of the leaves of the trees). Both hierarchies are conjectured to be infinite, and some results are presented concerning this conjecture. A study is made of the closure properties of the top-down and bottom-up families in the hierarchies under various tree and string operations. The families are shown to be closed under certain operations if and only if the hierarchies are finite.

Brenda S. Baker

Papers

Stable prehension with a multi-fingered hand

Approximation Algorithms for NP.Complete Problems on Planar Graphs (Preliminary Version

Tree transductions and families of tree languages

Generalized Syntax Directed Translation, Tree Transducers, and Linear Space

Tree transducers and tree languages