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The paper presents a botnet detection approach for the distributed systems. It is based on the developed three level model, which includes botnet’s components: command and control center, control centers, basic elements of the botnet (bots). The novel framework provides the ability to detect known and unknown botnets, and consists of the host and the network levels. At the host level, the detection procedure is based on the implementation of the Bayes classification. The network level extends the results obtained at the host level to the rest of the local area network. Proposed approach provides the exchange of the results obtained by the Bayes classification for further use by other program units of the distributed system. The results of the developed classifier show that representation of the botnets’ samples for different classes and subclasses is sufficient for efficient botnet detection. Proposed technique demonstrates promising results concerning botnet detection in the distributed systems.

This article presents the technique for botnet detection using the distributed systems in the local area network. Distributed system contains host and network levels. At the host level, the botnets detection is based on Bayes classification. In order to perform the classification, the classes and subclasses were constructed on the basis of botnets patterns. An algorithm for classifier training was developed. The network level provides the exchange of the classification results for the knowledge transfer to the rest of the antivirus program units of the distributed system.

Automated and semi-automated systems that derive actionable information from massive, heterogeneous datasets are essential for many applications. The reasoning of such systems must be as clear as possible in order to earn our trust. Lattices have begun to play a key role in computer science finding applications in distributed computing, programming languages, concurrency theory, and data mining, thereby justifying G. C. Rota's belief that lattice theory will play an important role in 21st Century mathematics [1]. In some instances, researchers must deal with posets that are not necessarily lattices and the question arises how these posets can be embedded in lattices. A classic way to answer this question is to construct the MacNeille completion of the lattice, which is the most compact way to embed a poset into a lattice. In 1973 G. Markowsky introduced the poset of irreducibles construction in his dissertation and demonstrated that this was a very compact way to represent a lattice. In addition, the poset of irreducibles has many of the properties of the poset of join-irreducibles of distributive lattices that was introduced by G. Birkhoff and described in his book [2]. In this paper, we show how to construct the poset of irreducibles for the MacNeille completion of a poset efficiently. We conclude with some applications of these ideas.

The paper proposes the architecture of a distributed malware detection system based on decentralized architecture in local area computer networks. Its feature is the synthesis of its requirements of distribution, decentralization, multilevel. This allows you to use it autonomously. In addition, the feature of the components of the system is the same organization, which allows the exchange of knowledge in the middle of the system, which, unlike the known systems, allows you to use the knowledge gained by separate parts of the system in other parts. The developed system allows to fill it with subsystems of detection of various types of malicious software in local area networks. The paper presents the results of experiments on the use of the developed system for the detection of metamorphic viruses.

The paper proposes the architecture of distributed multilevel detection system of malicious software in local area networks. Its feature is the synthesis of its requirements of distribution, decentralization, multilevel. This allows you to use it autonomously. In addition, the feature of autonomous program modules of the system is the same organization, which allows the exchange of knowledge in the middle of the system, which, unlike the known systems, allows you to use the knowledge gained by separate parts of the system in other parts. The developed system allows to fill it with subsystems of detection of various types of malicious software in local area networks.

This paper is an extension of my earlier paper [1]. It examines the continuing growth of this problem, and the likelihood that it will continue to get worse. Since the previous paper, the author was contacted by a lawyer involved in litigating a dispute related to TLDs. As noted in the previous paper, misdirected communication has obvious security and privacy ramifications and is an age old problem that predates the Internet. In recent years it has been exacerbated by the arrival of electronic communication and the multitude of ways that communication can be misdirected. A new chapter in this age old problem is being written with the proliferation of top level domains (TLDs). This paper examines this problem in more detail and provides a full analysis of the current set of TLDs. In particular, we are concerned with TLDs that have a nontrivial probability of intercepting traffic intended for another TLD. Intercepting TLDs have the potential of intercepting a lot of traffic since a TLD can support many domain names. This paper updates the results in the previous paper and also performs an auditory similarity measurement between domain names. The issue here is that sometimes TLDs are given orally, such as over the telephone. There are TLDs which, although spelled differently, sound similar to each other. Finally, we give the results of some experiments performed with purchased domain names to be deliberately confusing.

The Ternopil Educational Communication Center was developed with NATO funding to improve computing for the universities of Ternopil, Ukraine. It provides high speed access for all of Ternopil’s universities to the Internet and the World Wide Web. It enables high speed communication within Ternopil, and between institutions in Ternopil using the UarNet and URAN networks. It provides an integration of on-line library services, and it supports such activities as video conferencing, distance education, and class to class participation. The universities of Ternopil and the University of Maine are developing programs and projects to involve students and faculty both in Ukraine and the US.

This paper describes the Smart Vehicle Screening System, which can be installed into a tollbooth for automated recognition of vehicle license plate information using a photograph of a vehicle. An automated system could then be implemented to control the payment of fees, parking areas, highways, bridges or tunnels, etc. There are considered an approach to identify vehicle through recognizing of it license plate using image fusion, neural networks and threshold techniques as well as some experimental results to recognize the license plate successfully.

In this paper we examine the history of using random numbers in computer programs. Unfortunately, this history is sad because it is replete with disasters ranging from one of the first pseudo-random number generators, RANDU, beingverybadtothemostrecenteffortsbytheNSAtounderminethepseudorandom number generator in RSA’s BSAFE cryptographic library. Failures in this area have been both intentional and unintentional, but unfortunately the same sorts of mistakes are repeated. The repeated failures in getting our “randomnumbers”correctsuggeststhattheremightbesomesystemicreasons forthesefailures.Inthispaperwereviewsomeofthesefailuresinmoredetail, and the 2006 Debian OpenSSL Debacle in great detail. This last event left users of Debian and its derivatives with seriously compromised cryptographic capabilities for two years. We also illustrate how this failure can be exploited in an attack. We also modify the concept of a system accident developed in the work of Charles Perrow [1]. We identify some system failures in building pseudo-randomnumbergeneratorsandoffersomesuggestionstohelpdevelop PRNGs and other code more securely.

This article gives some background information on the authors’ forthcoming book, The State of Learning. There are many challenges facing educators who want to bring education into the 21st century. At the same time, the explosion of technology has the potential to make education more available and influential than ever before. Education is taking place on a large stage and is not just confined to schools. We must rethink the foundations of education so it can truly benefit from new technology.

Authors suggested the development of a specialized network interface for network of detectors that are part of alarm system. Providing a high level of network security against intruder is achieved using a large number of security elements and their dynamic change in on-line mode network operation. The proposed system uses traditional detectors; each is connected to the network through node based on a microcontroller. This allows connection of traditional detectors into two-wired network with common bus type and to reduce the number of wired lines without loss of system informative channels. An additional advantage is in powering sensors by a server via informational network channel.

We describe the recent developments of an open-source project called RATCHET that can be used by groups of users to collectively construct attack trees. We present the RATCHET framework as well as a model for testing and evaluation of the produced attack trees. RATCHET has been tested in classroom settings with positive results and this paper presents the plans for expanding its outreach to the community at large and building attack trees through crowdsourcing. This paper gives an overview of RATCHET and an introduction to its use.

Misdirected communication has obvious security and privacy ramifications and is an age old problem that predates the Internet. In recent years it has been exacerbated by the arrival of electronic communication and the multitude of ways that communication can be misdirected. A new chapter in this age old problem is being written with the proliferation of top level domains (TLDs). This paper examines this problem in more detail and provides a full analysis of the current set of TLDs. In particular, we are concerned with TLDs that have a non-trivial probability of intercepting traffic intended for another TLD. Intercepting TLDs have the potential of intercepting a lot of traffic since a TLD can support many domain names.

Many smart, resource-constrained, and seldom-updated devices in the Internet of Things present unanticipated vulnerabilities. The Internet Census 2012 scanned for such devices to construct its Carna Botnet, which then surveyed the entire IPv4 address space. This census provides an order of magnitude for the number of devices vulnerable to just one type of attack. Finally, three scans of different types demonstrate how to scan for vulnerable devices in the Internet of Things. The first uses Shodan to find vulnerable Cayman DSL routers; the second uses Masscan to find devices vulnerable to Heartbleed, and the third used Nmap and PFT to find and connect to vulnerable networked printers.

This paper discusses ways that crowdsourcing can help homeland security. It reviews some successes in this area, suggests some directions and points out some obstacles. Short abstract.

Enterprise Resource Planning (ERP) systems currently used by American businesses are unsuitable for adoption by small and medium size Chinese businesses. Cross-cultural issues include not only the obvious localization and interface language differences but also bearable implementation costs, culturally-specific management styles, and financial report format discrepancies. This paper discusses the cross-cultural issues that must be addressed to bridge the gap between American and Chinese ERP systems and presents a case study of an ERP system designed using scrum, an agile software engineering methodology, to meet this need.

In this paper we examine in detail the Debian OpenSSL Debacle from the perspectives of a system accident, a concept derived from the work of Charles Perrow [1]. This event left users of Debian and its derivatives with seriously compromised cryptographic capabilities. We identify some common failings that might be problematic in other software development projects and offers some suggestions to help develop code more securely.

At the 2009 IEEE International Conference on Technologies for Homeland Security the author presented a paper entitled “Comparing Apples to Oranges” which showed the fundamental problem of ranking assets on multiple-factors. In particular, the talk showed that programs like Carver2 cannot consistently order targets. In particular, the author contends that using a spreadsheet such as Excel™ permits users to do as good a job of assessing targets as more dedicated systems. To improve the usefulness of Excel™ for target selection, the author has written a module that permits the spreadsheet to identify Condorcet cycles so that users will get a more realistic understanding of the vulnerability of their various assets. This paper describes the theoretical basis for this module and illustrates its operation. This module is available from the author.

Bacteria are susceptible to phage (viral) infections. One of the most important properties of phages is host specificity. Phages can be so selective that they will distinguish varieties among apparently identical organisms. By exposing an isolate growing on the surface of an agar plate to a battery of different phages a pattern develops contingent on the susceptibility or resistance of the culture to the phages. A culture sensitive to a particular phage is destroyed and the destruction is manifested by areas devoid of bacterial growth. Using phages to differentiate bacteria is referred to as phage typing. Phage typing can be extremely important in many health situations because it can identify random, unrelated organisms as well as the isolates that are actually responsible for a given problem. Aside from relating an organism to an outbreak, this laboratory method can also be used for surveillance, assessing strain distribution, and ascertaining the effectiveness of therapeutic measures. Phage typing requires the use of a standard collection of dissimilar phages. In the process of developing a phage typing set, numerous phages are first isolated and tests are undertaken to determine if they are different and useful in delineating the types of organisms under study. To make the procedure more cost effective and less labor-intensive the final set is reduced to a manageable number with the assistance of a computer. Selecting a smallest phage typing set is an NP-hard combinatorial search problem so no efficient algorithm for finding it is believed to exist. However, with a powerful computer very good solutions and sometimes optimal solutions can be found by intelligent searching. Using a variety of heuristic techniques and a variety of computers small phage sets have been found previously for Salmonella, Escherichia coli, and Staphylococcus epidermidis. These programs have been rewritten to take advantage of the greater speed and address space of the IBM 3090. We are now able to obtain better results because searching can be done more exhaustively and are able to find optimal phage typing sets, something that we were not able to do with earlier programs running on less powerful computers. We are currently working on a phage typing set for Staphylococcus aureus. Besides finding optimal solutions we also tested a greedy algorithm. Our results suggest that the greedy algorithm works well and should enable us to solve very large problems using powerful computers.

(1992). Misconceptions about the Golden Ratio. The College Mathematics Journal: Vol. 23, No. 1, pp. 2-19.

This paper studies certain types of join and meet-irreducibles called coprimes and primes. These elements can be used to characterize certain types of lattices. For example, a lattice is distributive if and only if every join-irreducible is coprime. Similarly, a lattice is meet-pseudocomplemented if and only if each atom is coprime. Furthermore, these elements naturally decompose lattices into sublattices so that often properties of the original lattice can be deduced from properties of the sublattice. Not every lattice has primes and coprimes. This paper shows that lattices which are “long enough” must have primes and coprimes and that these elements and the resulting decompositions can be used to study such lattices. The length of every finite lattice is bounded above by the minimum of the number of meet-irreducibles (meet-rank) and the number of join-irreducibles (join-rank) that it has. This paper studies lattices for which length=join-rank or length=meet-rank. These are called p-extremal lattices and they have interesting decompositions and properties. For example, ranked, p-extremal lattices are either lower locally distributive (join-rank=length), upper locally distributive (meet-rank=length) or distributive (join-rank=meet-rank=length). In the absence of the Jordan-Dedekind chain condition, p-extremal lattices still have many interesting properties. Of special interest are the lattices that satisfy both equalities. Such lattices are called extremal; this class includes distributive lattices and the associativity lattices of Tamari. Even though they have interesting decompositions, extremal lattices cannot be characterized algebraically since any finite lattice can be embedded as a subinterval into an extremal lattice. This paper shows how prime and coprime elements, and the poset of irreducibles can be used to analyze p-extremal and other types of lattices. The results presented in this paper are used to deduce many key properties of the Tamari lattices. These lattices behave much like distributive lattices even though they violate the Jordan-Dedekind chain condition very strongly having maximal chains that vary in length from N-1 to N(N-1)/2 where N is a parameter used in the construction of these lattices.

This paper describes hardware implementations of crypto protocol elements for secured data communication in two wired networks of security system detectors. Those elements are basic to crypto protocol development for that type of network. In addition, hardware tools for the network controller and the network server that support this protocol were developed. These tools will allow us to test and debug the proposed security elements and the crypto protocol.

There are several target selection systems that use multiple factors to select the most probable targets. Factors can be such things as replacement costs, strategic importance, and psychological importance. These systems use these factors to rank potential targets in some order. It is clear that comparing disparate factors is very much like comparing apples and oranges. We show that in general, you can't compare apples and oranges and maintain logical consistency. Thus, every multi-factorial target rating system is limited in the accuracy of its rankings. We illustrate our results using the CARVER2™ program. We conclude with a discussion of how these multi-factor systems may best be used by planners despite their limitations.

This paper focuses on the problem of bounding fault detection probabilities in combinational circuits. Two algorithms, the complete cutting algorithm and the gate blocking algorithm, are presented that always produce true lower bounds on the detection probability of a fault. Both algorithms can be used to identify difficult-to-test faults and to quickly construct test sets for specific faults. Both algorithms have qualitative versions which provide insight into a circuit while avoiding arithmetic calculation. Both algorithms resulted from research in trying to determine the accuracy of the safety factor heuristic of Jacob Savir.

This paper describes two algorithms for optimizing the design of distributed perimeter security systems. The first algorithm is a straightforward algorithm whose primary purpose is to help us formulate the problem formally. The second algorithm, is a genetic algorithm. Both algorithms were incorporated into a new module for our distributed security systems CAD software. Tests of the module show that it produced better solutions more quickly than any other algorithms that are known to us.

This paper presents the development of a network capable application processor (NCAP) compatible with the IEEE1451 standard. Its features are an online, remote, real-time reprogramming mode and support of high-speed interfaces. The high-speed interfaces are implemented using a FPGA (field-programmable gate array). A novel design using a configuration controller and a FPGA provides robust interfaces and efficient FPGA usage. This paper also describes how our NCAP prototype can be used in an intelligent security system

The problems of American-Ukrainian School of Computer Sciences establishment are discussed in this paper.

This paper describes the design of a low-cost network controller that can be used to interface sensors to security systems. This controller can use either a two-wired network interface with reconfigurable structure or an open optical channel for data communication with the network server. This design reduces the cost of data communication channels between sensors and the controller.

Approximately 90% of the world's cargo is transported by container - some 200 million cargo containers are transported between the world's seaports each year, constituting the most critical component of global trade. Since $12.5 trillion worth of merchandise is traded worldwide, the task of protecting cargo containers is critical. Given that some containers also transport dangerous biological, chemical and radioactive materials it is clear that container security is of tremendous importance. On March 14, 2004 ten Israelis were killed in the port of Ashod by terrorists hidden in a secret compartment in a cargo container, so it is clear that terrorists have begun thinking about using cargo containers as a vehicle for their attacks. We propose determining the acoustic fingerprint of a cargo container when it is first loaded, and then determining its acoustic fingerprint at various places as it moves to its destination. A significant difference in the fingerprint will cause the cargo container to receive greater attention, and give some indication of the changes that have taken place in the container.

We introduce a method based on time delays between among Internet protocol packages is proposed and software for determination of attacking computer status is developed within its virtual connection with a victim computer. An attacking computer functioning in two modes is considered: direct connecting to the victim computer and connecting through the chains of intermediate computers.

We explore the problem of geographically locating IP addresses. Identifying the location of Web content on the Internet has several applications in the field of homeland security. A solution is proposed that uses the traceroute utility as a tool for collecting network information surrounding the target IP address, and the WHOIS database and hostname analysis are used to extract geographical information from the trace information. The approach is first evaluated as a single solution, traced from one computer, then again as a distributed solution, running multiple geographically and network-diverse traceroutes. The distributed approach reveals an increased certainty in the results

This paper presents an algorithm for determining whether a phenotype system has a factor-union representation, i.e., whether sets of properties (factors) can be assigned to alleles so that the phenotype of each genotype is determined by the union of the factor sets of the alleles. If such a representation is possible, the algorithm can construct one using p or fewer factors, where p is the number of phenotypes. Refinements to the algorithm are presented that often construct representations using few factors. An example is presented to show that some phenotype systems can be represented only by using almost as many factors as there are phenotypes in the system. Finally, it is shown that the problem of finding factor-union representations for multilocus systems reduces to the problem for 1-locus systems.

A phage typing set composed of 13 phages is described for characterizing Staphylococcus epidermidis. Isolates (372) from cases of bovine mastitis were used in this study. Of these, 350 or 94% were successfully delineated, and 63 phage types were observed. Twenty two cultures were not typeable.

Given an undirected distance graph G=(V, E, d) and a set S, where V is the set of vertices in G, E is the set of edges in G, d is a distance function which maps E into the set of nonnegative numbers and S?V is a subset of the vertices of V, the Steiner tree problem is to find a tree of G that spans S with minimal total distance on its edges. In this paper, we analyze a heuristic algorithm for the Steiner tree problem. The heuristic algorithm has a worst case time complexity of O(¦S¦¦V¦ 2) on a random access computer and it guarantees to output a tree that spans S with total distance on its edges no more than 2(1?1/l) times that of the optimal tree, where l is the number of leaves in the optimal tree.

This paper presents and explores a comprehensive mathematical model for human leukocyte antigen serology, based on a mathematical formalization of the concept of specificity. This model is general enough to take into account such factors as absorption, elution, cross-reactivity, and incomplete immunization. The paper includes a presentation of the relevant immunological background and a short discussion of the underlying computational difficulty of the basic problems. Upper and lower bounds are derived for the minimal number of specificities required to explain a given set of HLA reactions, and it is shown that the numbers of antibodies and antigens involved must be no less then this minimal number of specificities. Other techniques and theorems are also presented to aid in reducing and analyzing HLA reaction matrices.

This paper analyzes a method for identifying end-to-end connections in computer networks which is designed to provide reductions in the sizes of the packet headers and routing tables stored in the nodes. The method, known as Local Path ID Swapping, uses a shortened connection identifier, called the LPID, in the message headers and routing tables. In general, the LPID field is swapped in the message header from node to node along the path of the route. Some analytical results are presented for evaluating the important tradeoffs involved in LPID swapping. Most notable is the tradeoff between the size of the LPID field and the number of connections which can be defined in the network.

The class of lattices we are interested in (subprojective lattices), can be gotten by taking the MacNeille completions of the class of complemented, modular, atomic lattices. McLaughlin showed that subprojective lattices can be represented as the lattices of W-closed subspaces of a vector space U in duality with a vector space W. In this paper, we give a characterization of subprojective lattices in terms of atoms and dual atoms, by means of an incidence space satisfying self-dual axioms. In the finite-dimensional case, a subprojective lattice is projective, and hence our self-dual axioms characterize finite-dimensional projective spaces in terms of points and hyperplanes. No numerical parameters appear explicitly in these axioms. For each subprojective lattice L with at least three elements, we define a projective envelope P (L) for it. P (L) is a projective lattice and there is a natural inf-preserving injection of L into P (L). This injection has other important properties which we take as the definition of a geometric map. In the course of studying geometric maps, we obtain a lattice theoretic proof of Mackey's result that the join of a U-closed subspace of V and a finite-dimensional subspace is U-closed, where (U, V) form a dual pair of vector spaces over a division ring. Furthermore, we show that if L is a subprojective lattice, P a projective lattice, and ψ: L → P a geometric map, then P is isomorphic to the projective envelope P (L) of L. The paper presents many other properties of subprojective lattices. It concludes with a characterization of subprojective lattices which are also projective.

For a complete lattice L L , in which every element is a join of completely join-irreducibles and a meet of completely meet-irreducibles (we say L L is a jm-lattice) we define the poset of irreducibles P ( L ) P(L) to be the poset (of height one) J ( L ) ∪ M ( L ) ( J ( L ) J(L) \cup M(L)(J(L) is the set of completely join-irreducibles and M ( L ) M(L) is the set of completely meet-irreducibles) ordered as follows: a > P ( L ) b a{ > _{P(L)}}b if and only if a ∈ J ( L ) , b ∈ M ( L ) a \in J(L),b \in M(L) , and a ⪇ L b a \nleqslant { _L}b . For a jm-lattice L L , the automorphism groups of L L and P ( L ) P(L) are isomorphic, L L can be reconstructed from P ( L ) P(L) , and the irreducible factorization of L L can be gotten from the components of P ( L ) P(L) . In fact, we can give a simple characterization of the center of a jm-lattice in terms of its separators (or unions of connected components of P ( L ) P(L) ). Thus P ( L ) P(L) extends many of the properties of the poset of join-irreducibles of a finite distributive lattice to the class of all jm-lattices. We characterize those posets of height 1 which are P ( L ) P(L) for some jm-lattice L L . We also characterize those posets of height 1 which are P ( L ) P(L) for a completely distributive jm-lattice, as well as those posets which are P ( L ) P(L) for some geometric lattice L L . More generally, if L L is a complete lattice, many of the above arguments apply if we use “join-spanning” and “meet-spanning” subsets of L L , instead of J ( L ) J(L) and M ( L ) M(L) . If L L is an arbitrary lattice, the same arguments apply to “join-generating” and “meet-generating” subsets of L L .

It is shown that ψ ( n ) \psi (n) , the size of the free distributive lattice on n generators (which is the number of isotone Boolean functions on subsets of an n element set), satisfies \[ ψ ( n ) ⩽ 2 ( 1 + O ( log n / n ) ) ( n [ n / 2 ] ) . \psi (n) \leqslant {2^{(1 + O(\log \;n/n))\left ( {\begin {array}{*{20}{c}} n \\ {[n/2]} \\ \end {array} } \right )}}. \] This result is an improvement by a factor n \sqrt n in the 0 term of a previous result of Kleitman. In the course of deriving the main result, we analyze thoroughly the techniques used here and earlier by Kleitman, and show that the result in this paper is “best possible” (up to constant) using these techniques.

Mathematical Immunogenetics I argued for the development of mathematics as a language for immunogenetics. A three-fold factorization of a reaction matrix was seen to be the important form of a model of a first order immunogenetic system. In the present paper, results of the authors on determining this factorization are reworked from a physical perspective and presented in an algorithmic form that can be used to compute a labeling matrix from data. Computer programs to perform these computations are in preparation.

Given a sequence of positive weights, W=w 1?...?w n >0, there is a Huffman tree, T? ("T-up") which minimizes the following functions: max{d(wi)}; Σd(wi); Σf(d(wi)) w i(here d(w i) represents the distance of a leaf of weight w i to the root and f is a function defined for nonnegative integers having the property that g(x) = f(x + 1) ? f(x) is monotone increasing) over the set of all trees for W having minimal expected length. Minimizing the first two functions was first done by Schwartz [5]. In the case of codes where W is a sequence of probabilities, this implies that the codes based on T? have all their absolute central moments minimal. In particular, they are the least variance codes which were also described by Kou [3]. Furthermore, there exists a Huffman tree T?, ("T-down") which maximizes the functions considered above. However, if g(x) is monotone decreasing, T? and T?, respectively maximize and minimize Σf(d(wi) w i) over the set of all trees for W having minimal expected length. In addition, we derive a number of interesting results about the distribution of labels within Huffman trees. By suitable modifications of the usual Huffman tree construction, (see [1]) T? and T? can also be constructed in time O(n log n).

In an earlier paper, the authors presented an algorithm for finding all polyhedral solid objects with a given set of vertices and straight line edges (its wire frame). This paper extends the Wire Frame algorithm to find all solid polyhedral objects with a given set of two dimensional projections. These projections may contain depth information in the form of dashed and solid lines, may represent cross sections, and may be overall or detail views. The choice of labeling conventions in the projections determines the difficulty of the problem. It is shown that with certain conventions and projections the problem of fleshing out projections essentially reduces to the problem of fleshing out wire frames. Even if no labeling is used, the Projections algorithm presented here finds all solutions even though it is possible to construct simple examples with a very large number of solutions. Such examples have a large amount of symmetry and various accidental coincidences which typically do not occur in objects of practical interest. Because of its generality, the algorithm can handle pathological cases if they arise. This Projections algorithm, which has applications in the conversion of engineering drawings in a Computer Aided Design, Computer Aided Manufacturing (CADCAM) system, has been implemented. The algorithm has successfully found solutions to problems that are rather complex in terms of either the number of possible solutions or the inherent complexity of projections of objects of engineering interest.