Kevin J. Compton

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Verified

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• Ph.D.
• Professor Emeritus at University of Michigan

We present two conditional expectation bounds. In the first bound, $Z$ is a random variable with $0\leq Z\leq 1$, $U_i$ ($i<t$) are i.i.d. random objects with each $U_i\sim U$, and $W_i=\mathbf{E}[Z|U_i]$ are conditional expectations whose average is $W=(W_0+\cdots+W_{t-1})/t$. We show for $0<\varepsilon\leq 1$ that $\mathbf{E}[Z]\leq\mathbf{P}_U\{...

This paper introduces an SPA power attack on the 8-bit implementation of the Twofish block cipher. The attack is able to unequivocally recover the secret key even under substantial amounts of error. An initial algorithm is described using exhaustive search on error free data. An error resistant algorithm is later described. It employs several thres...

Many of the important decidability results in malware analysis are based Turing machine models of computation. We exhibit computational models which use more realistic assumptions about machine and attacker resources. While seminal results such as [1–5] remain true for Turing machines, we show under more realistic assumptions, important tasks are d...

We describe an SPA attack on an 8-bit smart card implementation of the Serpent block cipher. Our attack uses measurements taken during an on-the-∞y key expansion together with linearity in the cipher's key schedule algorithm to drastically reduce the search time for an initial key. An implementation flnds 256-bit keys in 3.736 ms on average. Our wo...

We describe an SPA power attack on an 8-bit implementation of AES. Our attack uses an optimized search of the key space to improve upon previous work in terms of speed, flexibility, and handling of data error. We can find a 128-bit cipher key in 16ms on average, with similar results for 192- and 256-bit cipher keys. The attack almost always produce...

We present SPHIN, a model checker for reconfigurable hybrid systems based on the model checker SPIN. We observe that physical (analog) mobility can be modeled in the same way as logical (discrete) mobility is modeled in the π-calculus by means of channel name passing. We chose SPIN because it supports channel name passing and can model reconfigurat...

In this paper we perform an asymptotic average case analysis of some of the most important steps of Gosper’s algorithm for indefinite summation of hypergeometric terms. The space of input functions of the algorithm is described in terms of urn models, and the analysis is performed by using specialized probabilistic transform techniques. We analyze...

In this paper, we present several probabilistic transforms related to classical urn models. These transforms render the dependent random variables describing the urn occupancies into independent random variables with appropriate distributions. This simplifies the analysis of a large number of problems for which a function under investigation depend...

UML has become a standard language for designing software systems. To help software developers design a correct UML model for a software system has become an important goal for many UML CASE tools. We propose a new UML virtual machine based on abstract state machines. We combine the UML meta-model, UML model and user objects model into one under th...

Latest research results have shown that requirements errors have a prolonged impact on software development and that they are more expensive to fix during later stages than early stages in software development. Use case diagrams in UML are used to give requirements for a software system, but all descriptions for each use case are written in informa...

Gosper's algorithm is an automatic procedure that provides an answer to the question if a sum of hypergeometric terms can be expressed as the difference of a hypergeometric term and a constant. In order to asses the practical applicability of the algorithm, it is important to know its expected running time. In this paper, an asymptotic average case...

In this paper, the possibility of verifying #-calculus processes via Promela translation is investigated. A general translation method from #-calculus processes to Promela models is presented and its usefulness is shown by performing verification tasks with translated #-calculus examples and SPIN. Model checking translated #-calculus processes in S...

We present combinatorial methods for computing the third support weight enumerators of the five doubly-even, self-dual [32,16,8] codes. The methods exploit relationships that exist between support weight enumerators and complete coset weight enumerators of a self-dual code.

State Machines can avoid this separation by unifying them into one model.

The Unified Modeling Language is becoming more and more popular in the software development. However because of its ambiguisity in its semantic model, few verification tool has been built. Abstract State Machines have been successfully applied in giving semantics for programming language like C. In this report, we try to use the Abstract State Mach...

The Unified Modeling Language has become widely accepted as a standard in software development. Several tools have been produced to support UML model validation. However most of them support either static or dynamic model checking; and no tools support to check both static and dynamic aspects of a UML model. But a UML model should include the stati...

We describe a combinatorial method for deriving linear equations, involving coefficients of generalized Hamming weight enumerators (GHWEs) of even isodual codes, that are linearly independent from the Klove (1992) identities. These equations can be combined with some other results derived by the first author to compute the complete set of GHWEs of...

The Unified Modeling Language has become widely accepted as a standard in software development. Several tools have been produced to support UML model validation. These tools translate a UML model into a validation language such as PROMELA. However they have some shortcomings: there is no proof of correctness (with respect to the UML semantics) for...

Logic is now widely recognized as one of the foundational disciplines of computing, and its applications reach almost every aspect of the subject, from software engineering and hardware to programming languages and AI. The Handbook of Logic in Computer Science is a multi-volume work covering all the major areas of application of logic to theoretica...

Introduction A class of structures obeys a 0--1 law if every first-order sentence has an asymptotic probability of 0 or 1 within the class. Techniques used to prove 0--1 laws are closely related to average-case analyses of algorithms. For example, Abiteboul, Compton and Vianu [1] showed that the 0--1 law for random relational structures (which incl...

7.28> A(nx) A(n) = 1 for all [some] x ? 1: (c) lim n!1 A(x n+1 ) A(x n ) = 1 for all [some] x ? 1: We also obtain further equivalent statements by replacing tx by t=x in (a), and nx by n=x in (b). Proof. Regarding the `for all x' versions one has (a) =) (b), (c). Likewise for the `for some x' versions. Also, in each case the `for all x' version imp...

We give a general introduction to cryptographic protocols and the kinds of attacks to which they are susceptible. We then present a framework based on linear logic programming for analyzing authentication protocols and show how various notions of attack are expressed in this framework.

The classical van der Waerden Theorem says that for every every finite set S of natural numbers and every k-coloring of the natural numbers, there is a monochromatic set of the form aS+b for some a ? 0 and b 0. I.e., monochromatism is obtained by a dilation followed by a translation. We investigate the effect of reversing the order of dilation and...

A class of finite structures has a 0--1 law with respect to a logic if every property expressible in the logic has a probability approaching a limit of 0 or 1 as the structure size grows. To formulate 0--1 laws for maps (i.e., embeddings of graphs in a surface), it is necessary to represent maps as logical structures. Three such representations are...

We extend the recent approach of Papadimitrou and Yannakakis that relates the approximation properties of optimization problems to their logical representation. Our work builds on results by Kolaitis and Thakur who sytematically studied the expressibility classes Max Sigma n and Max Pi n of maximization problems and showed that they form a short hi...

Using Feferman-Vaught techniques a condition on the fine spectrum of an admissible class of structures is found which leads to a first-order 0–1 law. The condition presented is best possible in the sense that if it is violated then one can find an admissible class with the same fine spectrum which does not have a first–order 0–1 law. If the conditi...

A class of structures has a 0--1 law when any property expressible in a certain logic has limiting probability 0 or 1 as the size of the structures tends to infinity. We prove 0--1 laws for classes of maps of a given genus. This is a joint work with E. Bender and B. Richmond [1]. 1. Definition of the problem Let S be a set of primitive elements cal...

The optimization of a large class of queries is explored, using a powerful normal form recently proven. The queries include the fixpoint and while queries, and an extension of while with arithmetic. The optimization method is evaluated using a probabilistic analysis. In particular, the average complexity of fixpoint and while is considered and some...

The relationship between counting functions and logical expressibility is explored. The most well studied class of counting functions is #P, which consists of the functions counting the accepting computation paths of a nondeterministic polynomial-time Turing machine. For a logicL, #Lis the class of functions on finite structures counting the tuples...

finitude P (E; N)(f) = 0 Q(Z; D)(f) = 0 P; Q polynomes sur C De facon 'equivalente, une fonction f(z) est D-finie si et seulement si le sous espace vectoriel sur le corps des fractions rationnelles C (Z) engendr'e par les D n (f); n 2 N est de dimension finie. Cette propri'et'e-d'efinition donne la cl'e de la plupart des propri'et'es de cloture de...

The relationship between counting functions and logical expressibility is explored. The most well studied class of counting functions is P, which consists of the functions counting the accepting computation paths of a nondeterministic polynomial-time Turing machine. For a logic L, L is the class of functions on finite structures (of a fixed signatu...

We consider multiprocessing systems where processes make independent, Poisson distributed resource requests with mean arrival time 1. We assume that resources are not released. It is shown that the expected deadlock time is never less than 1, no matter how many processes and resources are in the system. Also, the expected number of processes blocke...

Stratified least fixpoint logic, or SLFP, characterizes the expressibility of stratified logic programs and, in a different formulation, has been used as a logic of imperative programs. These two formulations of SLFP are proved to be equivalent. A complete sequent calculus with one infinitary rule is given for SLFP. It is argued that SLFP is the mo...

Process algebras such as Milner's Calculus of Communicating Systems (CCS) are universalist, i.e., they assume that there is a single universe in which expressions are to be interpreted. We begin an investigation of a model theoretic approach to concurrency in which there are many universes. The classical result reconciling the universalist and mode...

Existential least fixpoint logic (ELFP) is a logic with a least fixpoint operator but only existential quantification. It arises in many areas of computer science including logic programming, database theory, program verification, complexity theory, and recursion theory on abstract structures. A sequent calculus (Gentzen-style deductive system) for...

We give several characterizations, in terms of formal logic, semigroup theory, and operations on languages, of the regular languages in the circuit complexity class AC0, thus answering a question of Chandra, Fortune, and Lipton. As a by-product, we are able to determine effectively whether a given regular language is in AC0 and to solve in part an...

A proof is given of a result characterizing the regular languages in AC 0 , the class of problems accepted by constant depth families of circuits. A key part of this proof is much simpler than the original proof due to Barrington, Compton, Straubing and Thérien, who used deep results from monoid theory. The aim is to make results in this field more...

A new method for obtaining lower bounds on the computational complexity of logical theories is presented. It extends widely used techniques for proving the undecidability of theories by interpreting models of a theory already known to be undecidable. New inseparability results related to the well known inseparability result of Trakhtenbrot and Vaug...

Define [lambda](n) to be the largest integer such that for each set A of size n and cover J of A, there exist B [subset of or equal to] A and G [subset of or equal to] J such that |B| = [lambda](n) and the restriction of G to B is a partition of B. It is shown that when n [ges] 3. The lower bound is proved by a probabilistic method. A related proba...

This is a survey of logical results concerning random structures. A class of relational structures on which a (finitely additive) probability measure has been defined has a 0–1 law for a particular logic if every sentence of that logic has probability either 0 or 1. The measure may be an asymptotic probability on finite structures or generated on a...

An algebra and a logic characterizing the complexity class NC¹, which consists of functions computed by uniform sequences of polynomial-size, log depth circuits, are presented. In both characterizations, NC¹ functions are regarded as functions from one class of finite relational structures to another. In the algebraic characte...

The class of partial orders is shown to have 0-1 laws for first-order logic and for inductive fixed-point logic, a logic which properly contains first-order logic. This means that for every sentence in one of these logics the proportion of labeled (or unlabeled) partial orders of size n satisfying the sentence has a limit of either 0 or 1 as n goes...

Presented here are an algebra and a logic characterizing the complexity class NC1, which consists of functions computed by uniform families of polynomial size, log depth circuits. In both characterizations, NC1 functions are regarded as functions from one class of finite relational structures to another. In the algebraic characterization a recursio...

Results delimiting the logical and effective content of asymptotic combinatorics are presented. For the class of binary relations with an underlying linear order, and the class of binary functions, there are properties, given by first-order sentences, without asymptotic probabilities; every first-order asymptotic problem (i.e., set of first-order s...

Peer Reviewed http://deepblue.lib.umich.edu/bitstream/2027.42/26614/1/0000155.pdf

We shall present a general framework for dealing with an extensive set of problems from asymptotic combinatorics; this framework provides methods for determining the probability that a large, finite structure, ran- domly chosen from a given class, will have a given property. Our main concern is the asymptotic probability: the limiting value as the...

An extension of a Tauberian theorem of Hardy and Littlewood is proved. It is used to show that, for classes of finite models satisfying certain combinatorial and growth properties, Cesàro probabilities (limits of average probabilities over second order sentences) exist. Examples of such classes include the class of unary functions and the class of...

Problems of computing probabilities of statements about large, finite structures have become an important subject area of finite combinatorics. Within the last two decades many researchers have turned their attention to such problems and have developed a variety of methods for dealing with them. Applications of these ideas include nonconstructive e...

This chapter focuses on rich words. A structure consists of a set, called the universe of the structure, together with some relations, operations, and distinguished elements or constants from that set. The term structure is from model theory. A substructure of a structure A is a structure whose universe is a subset of the universe of A and whose re...

The study of preservation theorems for first order logic was the focus of much research by model theorists in the 1960's. These theorems, which came to form the foundation for classical model theory, characterize first order sentences and theories that are preserved under operations such as the taking of unions or submodels (see Chang and Keisler [...

Typescript. Thesis (Ph. D.)--University of Wisconsin--Madison, 1980. Vita. Includes bibliographical references (leaves 118-120).

A nonreactive orifice in an infinite baffle is analyzed. The pressure difference delta across the orifice varies sinusoidally with amplitude 1.0 and average value -P. The orifice resistance, delta p is discontinuous at zero velocity and exhibits the constant values R sub + and R sub - for u 0 and u 0, respectively. The resultant velocity has power...

Previous laboratory work has indicated that an orifice in a thin sheet behaves in a quasisteady manner under acoustical excitation. Also, it has been found that the steady flow resistance of an orifice may be dependent upon the direction of flow, especially in the presence of a crossflow on one side of the hole. An analytical study is presented whi...

A reconfigurable hybrid system is a collection of digital and analog components, where digital components are embedded in and interact with analog components and their configuration can be changed by means of physical or logical mobility of components. To establish a formal framework for the specification and verification of such systems, we extend...