Reasons for Hardness in QBF Proof Complexity

Quantified Boolean Formulas (QBF) extend the canonical NP-complete satisfiability problem by including Boolean quantifiers. Determining the truth of a QBF is PSPACE-complete; this is expected to be a harder problem than satisfiability, and hence QBF solving has much wider applications in practice. QBF proof complexity forms the theoretical basis for understanding QBF solving, as well as providing insights into more general complexity theory, but is less well understood than propositional proof complexity. We begin this thesis by looking at the reasons underlying QBF hardness, and in particular when the hardness is propositional in nature, rather than arising due to the quantifiers. We introduce relaxing QU-Res, a previous model for identifying such propositional hardness, and construct an example where relaxing QU-Res is unsuccessful in this regard. We then provide a new model for identifying such hardness which we prove captures this concept. Now equipped with a means of identifying ‘genuine’ QBF hardness, we prove a new lower bound technique for tree-like QBF proof systems. Lower bounds using this technique allows us to show a new separation between tree-like and dag-like systems. We give a characterisation of lower bounds for a large class of tree-like proof systems, in which such lower bounds play a prominent role. Further to the tree-like bound, we provide a new lower bound technique for QBF proof systems in general. This technique has some similarities to the above technique for tree-like systems, but requires some refinement to provide bounds for dag-like systems. We give applications of this new technique by proving lower bounds across several systems. The first such lower bounds are for a very simple family of QBFs. We then provide a construction to combine false QBFs to give formulas for which we can show lower bounds in this way, allowing the generation of the first random QBF proof complexity lower bounds

Certifying Correctness for Combinatorial Algorithms : by Using Pseudo-Boolean Reasoning

Over the last decades, dramatic improvements in combinatorialoptimisation algorithms have significantly impacted artificialintelligence, operations research, and other areas. These advances,however, are achieved through highly sophisticated algorithms that aredifficult to verify and prone to implementation errors that can causeincorrect results. A promising approach to detect wrong results is touse certifying algorithms that produce not only the desired output butalso a certificate or proof of correctness of the output. An externaltool can then verify the proof to determine that the given answer isvalid. In the Boolean satisfiability (SAT) community, this concept iswell established in the form of proof logging, which has become thestandard solution for generating trustworthy outputs. The problem isthat there are still some SAT solving techniques for which prooflogging is challenging and not yet used in practice. Additionally,there are many formalisms more expressive than SAT, such as constraintprogramming, various graph problems and maximum satisfiability(MaxSAT), for which efficient proof logging is out of reach forstate-of-the-art techniques.This work develops a new proof system building on the cutting planesproof system and operating on pseudo-Boolean constraints (0-1 linearinequalities). We explain how such machine-verifiable proofs can becreated for various problems, including parity reasoning, symmetry anddominance breaking, constraint programming, subgraph isomorphism andmaximum common subgraph problems, and pseudo-Boolean problems. Weimplement and evaluate the resulting algorithms and a verifier for theproof format, demonstrating that the approach is practical for a widerange of problems. We are optimistic that the proposed proof system issuitable for designing certifying variants of algorithms inpseudo-Boolean optimisation, MaxSAT and beyond

QBF Proof Complexity

Quantified Boolean Formulas (QBF) and their proof complexity are not as well understood as propositional formulas, yet remain an area of interest due to their relation to QBF solving. Proof systems for QBF provide a theoretical underpinning for the performance of these solvers. We define a novel calculus IR-calc, which enables unification of the principal existing resolution-based QBF calculi and applies to the more powerful Dependency QBF (DQBF). We completely reveal the relative power of important QBF resolution systems, settling in particular the relationship between the two different types of resolution-based QBF calculi. The most challenging part of this comparison is to exhibit hard formulas that underlie the exponential separations of the proof systems. In contrast to classical proof complexity we are currently short of lower bound techniques for QBF proof systems. To this end we exhibit a new proof technique for showing lower bounds in QBF proof systems based on strategy extraction. We also find that the classical lower bound techniques of the prover-delayer game and feasible interpolation can be lifted to a QBF setting and provide new lower bounds. We investigate more powerful proof systems such as extended resolution and Frege systems. We define and investigate new QBF proof systems that mix propositional rules with a reduction rule, we find the strategy extraction technique also works and directly lifts lower bounds from circuit complexity. Such a direct transfer from circuit to proof complexity lower bounds has often been postulated, but had not been formally established for propositional proof systems prior to this work. This leads to strong lower bounds for restricted versions of QBF Frege, in particular an exponential lower bound for QBF Frege systems operating with AC0[p] circuits. In contrast, any non-trivial lower bound for propositional AC0[p]-Frege constitutes a major open problem

Colour coded

This 300 word publication to be published by the Society of Dyers and Colourists (SDC) is a collection of the best papers from a 4-year European project that has considered colour from the perspective of both the arts and sciences.The notion of art and science and the crossovers between the two resulted in application and funding for cross disciplinary research to host a series of training events between 2006 and 2010 Marie Curie Conferences & Training Courses (SCF) Call Identifier: FP6-Mobility-4, Euros 532,363.80 CREATE – Colour Research for European Advanced Technology Employment. The research crossovers between the fields of art, science and technology was also a subject that was initiated through Bristol’s Festival if Ideas events in May 2009. The author coordinated and chaired an event during which the C.P Snow lecture “On Two Cultures’ (1959) was re-presented by Actor Simon Cook and then a lecture made by Raymond Tallis on the notion of the Polymath. The CREATE project has a worldwide impact for researchers, academics and scientists. Between January and October 2009, the site has received 221, 414 visits. The most popular route into the site is via the welcome page. The main groups of visitors originate in the UK (including Northern Ireland), Italy, France, Finland, Norway, Hungary, USA, Finland and Spain. A basic percentage breakdown of the traffic over ten months indicates: USA -15%; UK - 16%; Italy - 13%; France -12%; Hungary - 10%; Spain - 6%; Finland - 9%; Norway - 5%. The remaining approximate 14% of visitors are from other countries including Belgium, The Netherlands and Germany (approx 3%). A discussion group has been initiated by the author as part of the CREATE project to facilitate an ongoing dialogue between artists and scientists. http://createcolour.ning.com/group/artandscience www.create.uwe.ac.uk.Related papers to this research: A report on the CREATE Italian event: Colour in cultural heritage.C. Parraman, A. Rizzi, ‘Developing the CREATE network in Europe’, in Colour in Art, Design and Nature, Edinburgh, 24 October 2008.C. Parraman, “Mixing and describing colour”. CREATE (Training event 1), France, 2008

Mathematics & Statistics 2017 APR Self-Study & Documents

UNM Mathematics & Statistics APR self-study report, review team report, response report, and initial action plan for Spring 2017, fulfilling requirements of the Higher Learning Commission

Suicidal Utopian Delusions in the 21st Century: Philosophy, Human Nature and the Collapse of Civilization-- Articles and Reviews 2006-2017 2nd Edition Feb 2018

This collection of articles was written over the last 10 years and edited to bring them up to date (2019). All the articles are about human behavior (as are all articles by anyone about anything), and so about the limitations of having a recent monkey ancestry (8 million years or much less depending on viewpoint) and manifest words and deeds within the framework of our innate psychology as presented in the table of intentionality. As famous evolutionist Richard Leakey says, it is critical to keep in mind not that we evolved from apes, but that in every important way, we are apes. If everyone was given a real understanding of this (i.e., of human ecology and psychology to actually give them some control over themselves), maybe civilization would have a chance. As things are however the leaders of society have no more grasp of things than their constituents and so collapse into anarchy is inevitable. The first group of articles attempt to give some insight into how we behave that is reasonably free of theoretical delusions. In the next three groups, I comment on three of the principal delusions preventing a sustainable world— technology, religion and politics (cooperative groups). People believe that society can be saved by them, so I provide some suggestions in the rest of the book as to why this is unlikely via short articles and reviews of recent books by well-known writers. It is critical to understand why we behave as we do and so the first section presents articles that try to describe (not explain as Wittgenstein insisted) behavior. I start with a brief review of the logical structure of rationality, which provides some heuristics for the description of language (mind, rationality, personality) and gives some suggestions as to how this relates to the evolution of social behavior. This centers around the two writers I have found the most important in this regard, Ludwig Wittgenstein and John Searle, whose ideas I combine and extend within the dual system (two systems of thought) framework that has proven so useful in recent thinking and reasoning research. As I note, there is in my view essentially complete overlap between philosophy, in the strict sense of the enduring questions that concern the academic discipline, and the descriptive psychology of higher order thought (behavior). Once one has grasped Wittgenstein’s insight that there is only the issue of how the language game is to be played, one determines the Conditions of Satisfaction (what makes a statement true or satisfied etc.) and that is the end of the discussion. No neurophysiology, no metaphysics, no postmodernism, no theology. It is my contention that the table of intentionality (rationality, mind, thought, language, personality etc.) that features prominently here describes more or less accurately, or at least serves as an heuristic for, how we think and behave, and so it encompasses not merely philosophy and psychology, but everything else (history, literature, mathematics, politics etc.). Note especially that intentionality and rationality as I (along with Searle, Wittgenstein and others) view it, includes both conscious deliberative System 2 and unconscious automated System 1 actions or reflexes. The next section describes the digital delusions, which confuse the language games of System 2 with the automatisms of System one, and so cannot distinguish biological machines (i.e., people) from other kinds of machines (i.e., computers). The ‘reductionist’ claim is that one can ‘explain’ behavior at a ‘lower’ level, but what actually happens is that one does not explain human behavior but a ‘stand in’ for it. Hence the title of Searle’s classic review of Dennett’s book (“Consciousness Explained”)— “Consciousness Explained Away”. In most contexts ‘reduction’ of higher level emergent behavior to brain functions, biochemistry, or physics is incoherent. Even for ‘reduction’ of chemistry or physics, the path is blocked by chaos and uncertainty. Anything can be ‘represented’ by equations, but when they ‘represent’ higher order behavior, it is not clear (and cannot be made clear) what the ‘results’ mean. Reductionist metaphysics is a joke, but most scientists and philosophers lack the appropriate sense of humor. The last section describes The One Big Happy Family Delusion, i.e., that we are selected for cooperation with everyone, and that the euphonious ideals of Democracy, Diversity and Equality will lead us into utopia, if we just manage things correctly (the possibility of politics). Again, the No Free Lunch Principle ought to warn us it cannot be true, and we see throughout history and all over the contemporary world, that without strict controls, selfishness and stupidity gain the upper hand and soon destroy any nation that embraces these delusions. In addition, the monkey mind steeply discounts the future, and so we cooperate in selling our descendant’s heritage for temporary comforts, greatly exacerbating the problems. The only major change in this edition is the addition in the last article of a short discussion of China, a threat to peace and freedom as great as overpopulation and climate change and one to which even most professional scholars and politicians are oblivious so I regarded it as sufficiently important to warrant a new edition. I describe versions of this delusion (i.e., that we are basically ‘friendly’ if just given a chance) as it appears in some recent books on sociology/biology/economics. Even Sapolsky’s otherwise excellent “Behave”(2017) embraces leftist politics and group selection and gives space to a discussion of whether humans are innately violent. I end with an essay on the great tragedy playing out in America and the world, which can be seen as a direct result of our evolved psychology manifested as the inexorable machinations of System 1. Our psychology, eminently adaptive and eugenic on the plains of Africa from ca. 6 million years ago, when we split from chimpanzees, to ca. 50,000 years ago, when many of our ancestors left Africa (i.e., in the EEA or Environment of Evolutionary Adaptation), is now maladaptive and dysgenic and the source of our Suicidal Utopian Delusions. So, like all discussions of behavior (philosophy, psychology, sociology, biology, anthropology, politics, law, literature, history, economics, soccer strategies, business meetings, etc.), this book is about evolutionary strategies, selfish genes and inclusive fitness (kin selection, natural selection). The great mystic Osho said that the separation of God and Heaven from Earth and Humankind was the most evil idea that ever entered the Human mind. In the 20th century an even more evil notion arose, or at least became popular with leftists—that humans are born with rights, rather than having to earn privileges. The idea of human rights is an evil fantasy created by leftists to draw attention away from the merciless destruction of the earth by unrestrained 3rd world motherhood. Thus, every day the population increases by 200,000, who must be provided with resources to grow and space to live, and who soon produce another 200,000 etc. And one almost never hears it noted that what they receive must be taken from those already alive, and their descendants. Their lives diminish those already here in both major obvious and countless subtle ways. Every new baby destroys the earth from the moment of conception. In a horrifically overcrowded world with vanishing resources, there cannot be human rights without destroying the earth and our descendant’s futures. It could not be more obvious, but it is rarely mentioned in a clear and direct way, and one will never see the streets full of protesters against motherhood. The most basic facts, almost never mentioned, are that there are not enough resources in America or the world to lift a significant percentage of the poor out of poverty and keep them there. Even the attempt to do this is already bankrupting America and destroying the world. The earth’s capacity to produce food decreases daily, as does our genetic quality. And now, as always, by far the greatest enemy of the poor is other poor and not the rich. America and the world are in the process of collapse from excessive population growth, most of it for the last century, and now all of it, due to 3rd world people. Consumption of resources and the addition of 4 billion more ca. 2100 will collapse industrial civilization and bring about starvation, disease, violence and war on a staggering scale. The earth loses about 2% of its topsoil every year, so as it nears 2100, most of its food growing capacity will be gone. Billions will die and nuclear war is all but certain. In America, this is being hugely accelerated by massive immigration and immigrant reproduction, combined with abuses made possible by democracy. Depraved human nature inexorably turns the dream of democracy and diversity into a nightmare of crime and poverty. China will continue to overwhelm America and the world, as long as it maintains the dictatorship which limits selfishness. The root cause of collapse is the inability of our innate psychology to adapt to the modern world, which leads people to treat unrelated persons as though they had common interests (which I suggest may be regarded as an unrecognized -- but the commonest and most serious-- psychological problem -- Inclusive Fitness Disorder). This, plus ignorance of basic biology and psychology, leads to the social engineering delusions of the partially educated who control democratic societies. Few understand that if you help one person you harm someone else—there is no free lunch and every single item anyone consumes destroys the earth beyond repair. Consequently, social policies everywhere are unsustainable and one by one all societies without stringent controls on selfishness will collapse into anarchy or dictatorship. Without dramatic and immediate changes, there is no hope for preventing the collapse of America, or any country that follows a democratic system. Hence my concluding essay “Suicide by Democracy”. Those wishing to read my other writings may see Talking Monkeys 2nd ed (2019), The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle 2nd ed (2019), Suicide by Democracy 3rd ed (2019), The Logical Stucture of Human Behavior (2019) and Suicidal Utopian Delusions in the 21st Century 4th ed (2019

Suicidal Utopian Delusions in the 21st Century -- Philosophy, Human Nature and the Collapse of Civilization-- Articles and Reviews 2006-2019 4th Edition Michael Starks

The first group of articles attempt to give some insight into how we behave that is reasonably free of theoretical delusions. In the next three groups I comment on three of the principal delusions preventing a sustainable world— technology, religion and politics (cooperative groups). People believe that society can be saved by them, so I provide some suggestions in the rest of the book as to why this is unlikely via short articles and reviews of recent books by well-known writers. America and the world are in the process of collapse from excessive population growth, most of it for the last century and now all of it due to 3rd world people. Consumption of resources and the addition of 4 billion more ca. 2100 will collapse industrial civilization and bring about starvation, disease, violence and war on a staggering scale. Billions will die and nuclear war is all but certain. In America this is being hugely accelerated by massive immigration and immigrant reproduction, combined with abuses made possible by democracy. Depraved human nature inexorably turns the dream of democracy and diversity into a nightmare of crime and poverty. The root cause of collapse is the inability of our innate psychology to adapt to the modern world, which leads people to treat unrelated persons as though they had common interests. This, plus ignorance of basic biology and psychology, leads to the social engineering delusions of the partially educated who control democratic societies. Few understand that if you help one person you harm someone else—there is no free lunch and every single item anyone consumes destroys the earth beyond repair. Consequently social policies everywhere are unsustainable and one by one all societies without stringent controls on selfishness will collapse into anarchy or dictatorship. Without dramatic and immediate changes, there is no hope for preventing the collapse of America, or any country that follows a democratic system. Hence my concluding essay “Suicide by Democracy”. Those wishing to read my other writings may see Talking Monkeys 2nd ed (2019), The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle 2nd ed (2019), Suicide by Democracy 3rd ed (2019), The Logical Stucture of Human Behavior (2019) and Suicidal Utopian Delusions in the 21st Century 4th ed (2019

Suicidal Utopian Delusions in the 21st Century -- Philosophy, Human Nature and the Collapse of Civilization -- Articles and Reviews 2006-2019 4th Edition

The first group of articles attempt to give some insight into how we behave that is reasonably free of theoretical delusions. In the next three groups I comment on three of the principal delusions preventing a sustainable world— technology, religion and politics (cooperative groups). People believe that society can be saved by them, so I provide some suggestions in the rest of the book as to why this is unlikely via short articles and reviews of recent books by well-known writers. America and the world are in the process of collapse from excessive population growth, most of it for the last century and now all of it due to 3rd world people. Consumption of resources and the addition of 4 billion more ca. 2100 will collapse industrial civilization and bring about starvation, disease, violence and war on a staggering scale. Billions will die and nuclear war is all but certain. In America this is being hugely accelerated by massive immigration and immigrant reproduction, combined with abuses made possible by democracy. Depraved human nature inexorably turns the dream of democracy and diversity into a nightmare of crime and poverty. The root cause of collapse is the inability of our innate psychology to adapt to the modern world, which leads people to treat unrelated persons as though they had common interests. This, plus ignorance of basic biology and psychology, leads to the social engineering delusions of the partially educated who control democratic societies. Few understand that if you help one person you harm someone else—there is no free lunch and every single item anyone consumes destroys the earth beyond repair. Consequently social policies everywhere are unsustainable and one by one all societies without stringent controls on selfishness will collapse into anarchy or dictatorship. Without dramatic and immediate changes, there is no hope for preventing the collapse of America, or any country that follows a democratic system. Hence my concluding essay “Suicide by Democracy”