Michael Soltys

• PhD
• Chair at California State University, Channel Islands

Shortest path algorithms have played a key role in the past century, paving the way for modern day GPS systems to find optimal routes along static systems in fractions of a second. One application of these algorithms includes optimizing the total distance of power lines (specifically in star topological configurations). Due to the relevancy of disc...

This paper re-examines the content of a standard advanced course in Cybersecurity from the perspective of Cloud Computing. More precisely, we review the core concepts of Cybersecurity, as presented in a senior undergraduate or graduate class, in light of the Amazon Web Services (AWS) cloud.

The Cloud has become a principal paradigm of computing in the last ten years, and Computer Science curricula must be updated to reflect that reality. This paper examines simple ways to accomplish curriculum cloudification using Amazon Web Services (AWS), for Computer Science and other disciplines such as Business, Communication and Mathematics.

Faced with a preponderance of high capacity digital media devices, forensic investigators must be able to review them quickly, and establish which devices merit further attention. This early stage of an investigation is called triage and it is a chief part of evidence assessment; see [1, Chap. 2]. In this paper we present a digital forensic device,...

Attribution, the ability to match events on the Internet to actors who caused them, is a difficult problem in Cybersecurity and Digital Forensics. The Internet was not designed to track behavior of users [1]; instead, it is a common open platform that is propitious to anonymity. Different actors take advantage of this anonymity, and if they break t...

In the public imagination Cybersecurity is very much about malware, even though malware constitutes only part of all the threats faced by Cybersecurity experts. However, malware is still one of the best methods to gain persistent access and control of a target system. Malware is often combined with a well socially-engineered phishing attack that de...

This paper presents a senior undergraduate project which consists in the implementation of a Raspberry Pi based sprinkler system. The outcome is ingenious and innovative for several reasons: it is a low cost product, but of high quality and versatility (arguably better and cheaper than most household products on the market); it is well suited for u...

Compelling evidence against a heedless group theory generalization of pairwise comparisons elements is provided by means of counterexamples and mathematical reasoning. The lack of acceptable semantics for selected groups (with negative and complex numbers) and implications are analyzed. This study also provides examples and mathematical reasoning i...

Compelling evidence against a heedless group theory generalization of pairwise comparisons elements is provided by means of counter-examples and mathematical reasoning. The lack of acceptable semantics for selected groups (with negative and complex numbers) and implications are analyzed. This study also provides examples and mathematical reasoning...

We propose parametrized families of algorithms for approximating inconsistent matrices with consistent ones. We present experimental results, and optimize distance versus performance.

The threat of social engineering is one that affects not only the financial and reputational well-being of corporate entities but also the basic rights of individuals to privacy. Methods common to health campaigns used to disseminate information warning against social engineering have the potential for success. By providing potential scenarios and...

As our world of digital devices continues to expand, the amount of digital evidence encountered by law enforcement during case investigation is ever increasing. Faced with a preponderance of high capacity digital media devices, forensic investigators must be able to review them quickly, and establish which devices merit further attention. Utilizing...

A new formal framework for Stringology is proposed, which consists of a three-sorted logical theory S designed to capture the combinatorial reasoning about finite strings. We propose a language LS for expressing assertions about strings, and study in detail two sets of formulas Σ0B, a set of formulas decidable in polytime, and Σ1B, a set of formula...

Indeterminate strings have received considerable attention in the recent past; see for example [1] and [3]. This attention is due to their applicability in bioinformatics, and to the natural correspondence with undirected graphs. One aspect of this correspondence is the fact that the minimum alphabet size of indeterminates representing any given un...

The article shows a relationship between inconsistency in the pairwise comparisons method and conditions of order preservation. A pairwise comparisons matrix with elements from alo-group is investigated. This approach allows for generalization of the previous results. Sufficient conditions for order preservation based on the properties of elements...

This article explores a relationship between inconsistency in the pairwise comparisons method and conditions of order preservation. A pairwise comparisons matrix with elements from an alo-group is investigated. This approach allows for a generalization of previous results. Sufficient conditions for order preservation based on the properties of elem...

This book is a short introduction to the analysis of algorithms, from the point of view of proving algorithm correctness. The quote above refers to Mr. M'Choakumchild, a caricature of a teacher in Charles Dickens' Hard Times, who chokes the minds of his pupils with too much information. We will avoid M'Choakumchild's mistake, and make a virtue out...

In this study, we provide mathematical and practice-driven justification for using [0, 1]normalization of inconsistency indicators in pairwise comparisons. The need for normalization, as well as problems with the lack of normalization, is presented. A new type of paradox of infinity is described

Indeterminate strings have received considerable attention in the recent past; see for example Christodoulakis et al 2015 and Helling et al 2017. This attention is due to their applicability in bioinformatics, and to the natural correspondence with undirected graphs. One aspect of this correspondence is the fact that the minimal alphabet size of in...

In this study, we provide mathematical and practice-driven justification for using [0, 1] normalization of inconsistency indicators in pairwise comparisons. The need for normalization, as well as problems with the lack of normalization, are presented. A new type of paradox of infinity is described.

As discussed at length in [Christodoulakis et al., Indeterminate strings, prefix arrays and undirected graphs, Theoret. Comput. Sci. 600–4 (2015)], there is a natural one-many correspondence between simple undirected graphs with vertex set and indeterminate strings — that is, sequences of subsets of some alphabet Σ. In this paper, given , we consid...

In this study, we provide mathematical and practice-driven justification for using $[0,1]$ normalization of inconsistency indicators in pairwise comparisons. The need for normalization, as well as problems with the lack of normalization, are presented. A new type of paradox of infinity is described.

The paper is accepted for publication in the Special Issue of Fundamenta Informaticae: on Theory and Practice of Pairwise Comparison. This study has been inspired by numerous requests for clarification from researchers who often confuse Saaty's Analytic Hierarchy Process (AHP) with the pairwise comparisons (PC) method, taking AHP as the only repres...

We propose a research program for developing a formal framework for ranking procedures based on the Pairwise Comparisons method. We are interested in the case where relatively few items are to be ranked with a complex procedure and according to a large number of criteria. A typical example of this scenario is a competition where several companies b...

The pairwise comparisons method, together with inconsistency analysis, are used to assess the hazard level for abandoned mines. Weights, reflecting the relative importance of the objectives concerned are one of the most commonly used solutions for this type of data. Subjective assessments involve inaccuracy (which is difficult to manage) and incons...

This study has been inspired by numerous requests for clarification from researchers who often confuse Saaty's Analytic Hierarchy Process (AHP) with the pairwise comparisons (PC) method, taking AHP as the only representation of PC. This study should be regarded as an interpretation and clarification of past investigations of PC. In addition, this a...

A formal framework for ranking procedures is proposed. The case of interest is where relatively few items are to be ranked with a complex procedure and according to a large number of criteria. A typical example of this scenario is a competition where several companies bid for a contract, and where the selection of the winner is done with multiple c...

A word is non-repetitive if it does not contain a subword of the form vv. Given a list of alphabets L?=?L1,L2,?,Ln , we investigate the question of generating non-repetitive words w?=?w1w2?wn , such that the symbol wi is a letter in the alphabet Li . This problem has been studied by several authors (e.g., [GKM10], [Sha09]), and it is a natural exte...

We show that shuffle, the problem of determining whether a string w can be composed from an order preserving shuffle of strings x and y, is not in , but it is in . The fact that shuffle is not in is shown by a reduction of parity to shuffle and invoking the seminal result of Furst et al., while the fact that it is in is implicit in the results of M...

Fair and transparent procurement procedures are a cornerstone of a well functioning free-market economy. In particular, bidding is a mechanism whereby companies compete for contracts; when functioning well, the process rewards both the quality of the proposal, and the " reasonableness " of the quote. This way, both the company and the public win. T...

We show that Shuffle(x,y,w), the problem of determining whether a string w can be composed from an order preserving shuffle of strings x and y, is not in AC 0, but it is in AC 1. The fact that shuffle is not in AC 0 is shown by a reduction of parity to shuffle and invoking the seminal result [FSS84, while the fact that it is in AC 1 is implicit in...

We show that the well-known Konig's Min-Max Theorem (KMM), a fundamental result in combinatorial matrix theory, can be proven in the first order theory $\LA$ with induction restricted to $\Sigma_1^B$ formulas. This is an improvement over the standard textbook proof of KMM which requires $\Pi_2^B$ induction, and hence does not yield feasible proofs...

We show that the well-known Konig's Min-Max Theorem (KMM), a fundamental result in combinatorial matrix theory, can be proven in the first order theory $\LA$ with induction restricted to $\Sigma_1^B$ formulas. This is an improvement over the standard textbook proof of KMM which requires $\Pi_2^B$ induction, and hence does not yield feasible proofs...

A shuffle of two strings is formed by interleaving the characters into a new string, keeping the characters of each string in order. A string is a square if it is a shuffle of two identical strings. There is a known polynomial time dynamic programming algorithm to determine if a given string z is the shuffle of two given strings x,y; however, it ha...

We prove assorted properties of matrices over ${\mathbb{Z}_{2}}$ , and outline the complexity of the concepts required to prove these properties. The goal of this line of research is to establish the proof complexity of matrix algebra. It also presents a different approach to linear algebra: one that is formal, consisting in algebraic manipulatio...

In this paper we are concerned with computer science students' perceptions of foundational knowledge, understood as the mathematical underpinnings of the field. We review recent literature on the subject, propose an approach for teaching foundational knowledge, and finally present a case study where we analyze the merits of our approach. We make ou...

We investigate different variants of unambiguity in the con-text of computing multi-valued functions. We propose a modification to the standard computation models of Turing Machines and configuration graphs, which allows for unambiguity-preserving composition. We define a notion of reductions (based on function composition), which allows non-determ...

A successor to the first edition, this updated and revised book is a great companion guide for students and engineers alike, specifically software engineers who design reliable code. While succinct, this edition is mathematically rigorous, covering the foundations of both computer scientists and mathematicians with interest in algorithms. Besides c...

This paper is concerned with the complexity of computing winning strategies for poset games. While it is reasonably clear that such strategies can be computed in PSPACE, we give a simple proof of this fact by a reduction to the game of geography. We also show how to formalize the reasoning about poset games in Skelley’s theory for PSPACE reasoning....

We introduce the inverted prefix tries (a variation of suffix tries) as a convenient formalism for stating and proving properties of the Ehrenfeucht–Mycielski sequence [A. Ehrenfeucht, J. Mycielski, A pseudorandom sequence—how random is it? American Mathematical Monthly 99 (1992) 373-375]. We also prove an upper bound on the position in the sequenc...

This textbook covers the mathematical foundations of the analysis of algorithms. The gist of the book is how to argue, without the burden of excessive formalism, that a given algorithm does what it is supposed to do. The two key ideas of the proof of correctness, induction and invariance, are employed in the framework of pre/post-conditions and loo...

Given a separable polynomial p(x) 2 Q(x), which splits in R(x), is it possible to nd a symmetric matrix over Q whose eigenvalues are precisely the roots of p(x)? This note investigates this questions, and provides a condition on p(x) under which it is always possible to nd such a matrix| the question whether such a matrix can be found unconditional...

Although a deterministic polytime algorithm for primality testing is now known, the Rabin-Miller randomized test of primality continues being the most efficient and widely used algorithm. We prove the correctness of the Rabin-Miller algorithm in the theory V1 for polynomial time reasoning, from Fermat's little theorem. This is interesting because t...

The 2005 Franco-Canadian Workshop on Combinatorial Algorithms was held at Mc-Master University (Hamilton, Ontario, Canada) from August 18th to 20th. As the name suggests, the workshop intends to celebrate the long tradition of scientific and cultural connections between Canada and France. The workshop consisted of three days of plenary and contribu...

We introduce a new propositional proof system, which we call H, that allows quantifi- cation over permutations. In H we may write (9ab)� and (8ab)�, which is semantically equivalent to �(a,b) _ �(b,a) and �(a,b) ^ �(b,a), respectively. We show that H with cuts restricted to �1 formulas (we denote this system H1) simulates efficiently the Hajos calc...

We show that the logical theory QLA proves the Cayley-Hamilton theorem front the Steinitz exchange theorem together with a strengthening of the linear independence principle. Since QLA is a fairly weak theory (in the sense that its quantifier-free fragment, LA, translates into tautologies with TC(0)-Frege proofs-when restricted to the field 0 of th...

This paper has illustrated why, a course on these topics should be required as part of the basic science component of a programme for engineers specialising in software intensive products

LA is a simple and natural logical system for reasoning about matrices. We show that LA, over finite fields, proves a host of matrix identities (so-called "hard matrix identities") from the matrix form of the pigeonhole principle. LAP is LA with matrix powering; we show that LAP extended with quantification over permutations is strong enough to pro...

We show that Csanky’s fast parallel algorithm for computing the characteristic polynomial of a matrix can be formalized in the logical theory LAP, and can be proved correct in LAP from the principle of linear independence. LAP is a natural theory for reasoning about linear algebra introduced in[8]. Further, we show that several principles of matrix...

We investigate the theories of linear algebra, which were originally defined to study the question of whether commutativity of matrix inverses has polysize Frege proofs. We give sentences separating quantified versions of these theories, and define a fragment in which we can interpret a weak theory V 1 of bounded arithmetic and carry out polynomial...

We show that short bounded-depth Frege proofs of matrix identities, such as PQ= I? QP= I (over the field of two elements), imply short bounded-depth Frege proofs of the pigeonhole principle. Since the latter principle is known to require exponential-size bounded-depth Frege proofs, it follows that the propositional version of the matrix principle a...

Propositional proof complexity is a well established area of theoretical computer science; it is an area of research intimately connected with complexity theory and automated reasoning. In this paper we introduce a proof system, which we call A (a fragment of the theory LA), for formalizing algebraic proofs over arbitrary fields, and we show how to...

A combinatorial interpretation of Berkowitz's algorithm is presented. Berkowitz's algorithm is the fastest known parallel algorithm for computing the characteristic polynomial of a matrix. The combinatorial interpretation is based on "loop covers" introduced by Valiant, and "clow sequences", defined by Mahajan and Vinay. Clow sequences turn out to...

We introduce three formal theories of increasing strength for linear algebra in order to study the complexity of the concepts needed to prove the basic theorems of the subject. We give what is apparently the first feasible proofs of the Cayley-Hamilton theorem and other properties of the determinant, and study the propositional proof complexity of...

We present a combinatorial interpretation of Berkowitz's algorithm. Berkowitz's algorithm is the fastest known parallel algorithm for computing the characteristic polynomial of a matrix. Our combinatorial interpretation is based on ``loop covers'' introduced by Valiant, and ``clow sequences.'' Clow sequences turn out to capture very succinctly the...

We show that the Gaussian elimination algorithm can be proven correct with uniform extended Frege proofs of polynomial size, and hence feasibly. More precisely, we give short uniform extended Frege proofs of the tautologies that express the following: given a matrix A, the Gaussian elimination algorithm reduces A to row-echelon form. We also show t...

Michael Soltys-Kulinicz Doctor of Philosophy Graduate Department of Mathematics University of Toronto 2001 In this thesis we are concerned with building logical foundations for Linear Algebra, from the perspective of proof complexity. As the cornerstone of our logical theories, we use Berkowitz's parallel algorithm for computing the coecients of th...

We introduce the notion of Boolean programs, which provide more concise descriptions of Boolean functions than Boolean circuits. We characterize nonuniform PSPACE in terms of polynomial size families of Boolean programs. We then show how to use Boolean programs to witness quantifiers in the subsystems G1 and G 1 of the proof system G for the quanti...

We show that the Gaussian Elimination algorithm can be proven correct with uniform Extended Frege proofs of polynomial size, and hence feasibly. More precisely, we give short uniform Extended Frege proofs of the tautologies that express the following: given a matrix A, the Gaussian Elimination algorithm reduces A to row-echelon form. We also show t...

We show that Shuffle(x, y, w), the problem of determining whether a string w can be composed from an order preserving shuffle of strings x and y, is not in AC 0 , but it is in AC 1 . This provides a very tight complexity bound for this combinatorial problem. A consequence is that shuffle can be solved in parallel with polynomially many processors i...