A Graph Traversal Based Framework for Sequential Logic Implication with an Application to C-Cycle Redundancy Identification

Coordinated Science Laboratory was formerly known as Control Systems LaboratorySemiconductor Research Corporation / SRC 96-DP-109 and SRC 97-DS-482DARPA / DABT63-95-C-0069Hewlett-Packar

Transition to Higher Mathematics: Structure and Proof (Second Edition)

This book is written for students who have taken calculus and want to learn what “real mathematics is. We hope you will find the material engaging and interesting, and that you will be encouraged to learn more advanced mathematics. This is the second edition of our text. It is intended for students who have taken a calculus course, and are interested in learning what higher mathematics is all about. It can be used as a textbook for an Introduction to Proofs course, or for self-study. Chapter 1: Preliminaries, Chapter 2: Relations, Chapter 3: Proofs, Chapter 4: Principles of Induction, Chapter 5: Limits, Chapter 6: Cardinality, Chapter 7: Divisibility, Chapter 8: The Real Numbers, Chapter 9: Complex Numbers. The last 4 chapters can also be used as independent introductions to four topics in mathematics: Cardinality; Divisibility; Real Numbers; Complex Numbers.https://openscholarship.wustl.edu/books/1010/thumbnail.jp

The four color theorem: from graph theory to proof assistants.

openLa tesi inizialmente descrive i fondamenti della teoria dei grafi con le principali nozioni per affrontare il teorema dei sei, cinque e infine dei quattro colori. Quest'ultimo viene descritto dal punto di vista storico e viene fornita una traccia della dimostrazione, per poi indagare gli aspetti legati all'utilizzo di proof assistant.First, it describes the basic notions of graph theory in order to face the six, five and finally the four color theorem. This last problem is treated from an historical point of view and the main steps of the proof are given. Finally, some aspects linked to proof assistants are examine

Normalisation in Deep Inference

Στην διπλωματική αυτή εργασία γίνεται μια αναλυτική παρουσίαση του λογισμού των δομών, ενός φορμαλισμού της θεωρίας αποδείξεων που χρησιμοποιεί deep inference. Αυτό σημαίνει ότι οι συμπερασματικοί κανόνες εφαρμόζονται οσοδήποτε βαθιά στην πολυπλοκότητα ενός τύπου. Έπεται ότι οι αποδείξεις έχουν συμμετρική αντί για δενδρική μορφή. Εισάγουμε ένα σύστημα για την κλασική πρωτοβάθμια λογική και το συγκρίνουμε με το αντίστοιχο στον λογισμό ακολουθητών. Βλέπουμε πως επιτυγχάνεται τοπικότητα, δηλαδή κάθε λογικός κανόνας έχει σταθερή πολυπλοκότητα. Η εργασία τελικά εστιάζει στους διάφορους ορισμούς της κανονικής μορφής μιας απόδειξης.In this thesis we present the calculus of structures, a proof-theoretic formalism using deep inference. This means that inference rules apply arbitrarily deep inside formulas. It follows that derivations are now symmetric instead of tree-shape objects. A system for classical predicate logic is introduced and compared with the corresponding sequent calculus system. They both have an admissible Cut rule. However, locality can be obtained with deep inference, meaning that the effort of applying a rule is always bounded. Then we investigate what normal forms of deductions have been defined. Besides cut elimination, we can adopt two other notions of normalisation that allow cuts inside a derivation, under some constraints. We will try to remark common things and differences between normalisation in deep and shallow inference

Transformation of cryptographic primitives: provable security and proof presentation

We analyse transformations between cryptographic primitives and, for each transformation, we do two studies: its provable security (proving that if the original cryptographic primitive is secure, then the transformed cryptographic primitive is also secure); its proof presentation (exploring improved ways of presenting the proof). Our contributions divide into two sets: security proofs (sometimes new proofs and sometimes variants of known proofs); proof presentations (inspired by our security proofs) and extraction of lessons learned from them

Inquisitive Pattern Recognition

The Department of Defense and the Department of the Air Force have funded automatic target recognition for several decades with varied success. The foundation of automatic target recognition is based upon pattern recognition. In this work, we present new pattern recognition concepts specifically in the area of classification and propose new techniques that will allow one to determine when a classifier is being arrogant. Clearly arrogance in classification is an undesirable attribute. A human is being arrogant when their expressed conviction in a decision overstates their actual experience in making similar decisions. Likewise given an input feature vector, we say a classifier is arrogant in its classification if its veracity is high yet its experience is low. Conversely a classifier is non-arrogant in its classification if there is a reasonable balance between its veracity and its experience. We quantify this balance and we discuss new techniques that will detect arrogance in a classifier. Inquisitiveness is in many ways the opposite of arrogance. In nature inquisitiveness is an eagerness for knowledge characterized by the drive to question to seek a deeper understanding and to challenge assumptions. The human capacity to doubt present beliefs allows us to acquire new experiences and to learn from our mistakes. Within the discrete world of computers, inquisitive pattern recognition is the constructive investigation and exploitation of conflict in information. This research defines inquisitiveness within the context of self-supervised machine learning and introduces mathematical theory and computational methods for quantifying incompleteness that is for isolating unstable, nonrepresentational regions in present information models