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This paper describes a memory management discipline for programs that perform dynamic memory allocation and de-allocation. At runtime, all values are put into regions. The store consists of a stack of regions. All points of region allocation and deallocation are inferred automatically, using a type and effect based program analysis. The scheme does not assume the presence of a garbage collector. The scheme was first presented by Tofte and Talpin (1994); subsequently, it has been tested in The ML Kit with Regions, a region-based, garbage-collection free implementation of the Standard ML Core language, which includes recursive datatypes, higher-order functions and updatable references (Birkedal et al. 96, Elsman and Hallenberg 95). This paper defines a region-based dynamic semantics for a skeletal programming language extracted from Standard ML. We present the inference system which specifies where regions can be allocated and de-allocated and a detailed proof that the system is sound wi...

a coloring is called the chromatic number of�, and is usually denoted by��.Determining the chromatic number of a graph is known to be NP-hard (cf. [19]). Besides its theoretical significance as a canonical NPhard problem, graph coloring arises naturally in a variety of applications such as register allocation [11, 12, 13] is the maximum degree of any vertex. Be-and timetable/examination scheduling [8, 40]. In many We consider the problem of coloring�-colorable graphs with the fewest possible colors. We give a randomized polynomial time algorithm which colors a 3-colorable graph on vertices with� � ���� colors where sides giving the best known approximation ratio in terms of, this marks the first non-trivial approximation result as a function of the maximum degree. This result can be generalized to�-colorable graphs to obtain a coloring using�� � ��� � � � �colors. Our results are inspired by the recent work of Goemans and Williamson who used an algorithm for semidefinite optimization problems, which generalize linear programs, to obtain improved approximations for the MAX CUT and MAX 2-SAT problems. An intriguing outcome of our work is a duality relationship established between the value of the optimum solution to our semidefinite program and the Lovász�-function. We show lower bounds on the gap between the optimum solution of our semidefinite program and the actual chromatic number; by duality this also demonstrates interesting new facts about the�-function. 1

Representing and reasoning about incomplete and indefinite qualitative temporal information is an essential part of many artificial intelligence tasks. An interval-based framework and a point-based framework have been proposed for representing such temporal information. In this paper, we address two fundamental reasoning tasks that arise in applications of these frameworks: Given possibly indefinite and incomplete knowledge of the relationships between some intervals or points, (i) find a scenario that is consistent with the information provided, and (ii) find the feasible relations between all pairs of intervals or points. For the point-based framework and a restricted version of the intervalbased framework, we give computationally efficient procedures for finding a consistent scenario and for finding the feasible relations. Our algorithms are marked improvements over the previously known algorithms. In particular, we develop an O(n 2 ) time algorithm for finding one co...

Watermarking embeds a secret message into a cover message. In media watermarking the secret is usually a copyright notice and the cover a digital image. Watermarking an object discourages intellectual property theft, or when such theft has occurred, allows us to prove ownership. The Software Watermarking problem can be described as follows. Embed a structure W into a program P such that: W can be reliably located and extracted from P even after P has been subjected to code transformations such as translation, optimization and obfuscation; W is stealthy; W has a high data rate; embedding W into P does not adversely affect the performance of P ; and W has a mathematical property that allows us to argue that its presence in P is the result of deliberate actions. In the first part of the paper we construct an informal taxonomy of software watermarking techniques. In the second part we formalize these results. Finally, we propose a new software watermarking technique in which a dynamic gr...

Abstract. This paper presents a new approach to finding minimum cuts in undirected graphs. The fundamental principle is simple: the edges in a graph’s minimum cut form an extremely small fraction of the graph’s edges. Using this idea, we give a randomized, strongly polynomial algorithm that finds the minimum cut in an arbitrarily weighted undirected graph with high probability. The algorithm runs in O(n 2 log 3 n) time, a significant improvement over the previous Õ(mn) time bounds based on maximum flows. It is simple and intuitive and uses no complex data structures. Our algorithm can be parallelized to run in �� � with n 2 processors; this gives the first proof that the minimum cut problem can be solved in ���. The algorithm does more than find a single minimum cut; it finds all of them. With minor modifications, our algorithm solves two other problems of interest. Our algorithm finds all cuts with value within a multiplicative factor of � of the minimum cut’s in expected Õ(n 2 � ) time, or in �� � with n 2 � processors. The problem of finding a minimum multiway cut of a graph into r pieces is solved in expected Õ(n 2(r�1) ) time, or in �� � with n 2(r�1) processors. The “trace ” of the algorithm’s execution on these two problems forms a new compact data structure for representing all small cuts and all multiway cuts in a graph. This data structure can be efficiently transformed into the

A general automaton model for timing-based systems is presented and is used as the context for developing a variety of simulation proof techniques for such systems. As a first step, a comprehensive overview of simulation techniques for simple untimed automata is given. In particular, soundness and completeness results for (1) refinements, (2) forward and backward simulations, (3) forward-backward and backward-forward simulations, and (4) history and prophecy relations are given. History and prophecy relations are new and are abstractions of the history variables of Owicki and Gries and the prophecy variables of Abadi and Lamport, respectively. As a subsequent step, it is shown how most of the results for untimed automata can be carried over to the setting of timed automata. In fact, many of the results for the timed case are obtained as consequences of the analogous results for the untimed case.

We use random sampling as a tool for solving undirected graph problems. We show that the sparse graph, or skeleton, that arises when we randomly sample a graph’s edges will accurately approximate the value of all cuts in the original graph with high probability. This makes sampling effective for problems involving cuts in graphs. We present fast randomized (Monte Carlo and Las Vegas) algorithms for approximating and exactly finding minimum cuts and maximum flows in unweighted, undirected graphs. Our cut-approximation algorithms extend unchanged to weighted graphs while our weighted-graph flow algorithms are somewhat slower. Our approach gives a general paradigm with potential applications to any packing problem. It has since been used in a near-linear time algorithm for finding minimum cuts, as well as faster cut and flow algorithms. Our sampling theorems also yield faster algorithms for several other cut-based problems, including approximating the best balanced cut of a graph, finding a k-connected orientation of a 2k-connected graph, and finding integral multicommodity flows in graphs with a great deal of excess capacity. Our methods also improve the efficiency of some parallel cut and flow algorithms. Our methods also apply to the network design problem, where we wish to build a network satisfying certain connectivity requirements between vertices. We can purchase edges of various costs and wish to satisfy the requirements at minimum total cost. Since our sampling theorems apply even when the sampling probabilities are different for different edges, we can apply randomized rounding to solve network design problems. This gives approximation algorithms that guarantee much better approximations than previous algorithms whenever the minimum connectivity requirement is large. As a particular example, we improve the best approximation bound for the minimum k-connected subgraph problem from 1.85 to 1 � O(�log n)/k).

In this paper we formalise data models that are based on the concept of predicator, the combination of an object type and a role. A very simple model, the Predicator Model, is introduced in a rigid formal way. We introduce the concept of population as an instantiation of an information structure. A primitive manipulation language is defined in the style of relational algebra. Well-known types of constraints are defined in terms of the algebra introduced, as restrictions on populations. They are given more expressive power than is usually the case. Constraints are of central importance for identification purposes. Weak identification ensures identifiability of objects within a specific population, while structural identification ensures identifiability of objects within every population. Different levels of constraint inconsistency are defined and it is shown that the verification of two important levels is NP-complete.

Counting classes consist of languages defined in terms of the number of accepting computations of nondeterministic polynomial-time Turing machines. Well known examples of counting classes are NP, co-NP, \PhiP, and PP. Every counting class is a subset of P #P[1] , the class of languages computable in polynomial time using a single call to an oracle capable of determining the number of accepting paths of an NP machine. Using closure properties of #P, we systematically develop a complexity theory for counting classes defined in terms of thresholds and moduli. An unexpected result is that MOD k iP = MOD k P for prime k. Finally, we improve a result of Cai and Hemachandra by showing that recognizing languages in the class Few is as easy as distinguishing uniquely satisfiable formulas from unsatisfiable formulas (or detecting unique solutions, as in [28]). 1. Introduction Valiant [27] defined the class #P of functions whose values equal the number of accepting paths of polynomial-time bo...