Sequential decomposition of propositional logic programs

The sequential composition of propositional logic programs has been recently introduced. This paper studies the sequential {\em decomposition} of programs by studying Green's relations $\mathcal{L,R,J}$ -- well-known in semigroup theory -- between programs. In a broader sense, this paper is a further step towards an algebraic theory of logic programming.Comment: arXiv admin note: text overlap with arXiv:2109.05300, arXiv:2009.0577

Quarks and Leptons between Branes and Bulk

We study a supersymmetric SO(10) gauge theory in six dimensions compactified on an orbifold. Three sequential quark-lepton families are localized at the three fixpoints where SO(10) is broken to its three GUT subgroups. Split bulk multiplets yield the Higgs doublets of the standard model and as additional states lepton doublets and down-quark singlets. The physical quarks and leptons are mixtures of brane and bulk states. The model naturally explains small quark mixings together with large lepton mixings in the charged current. A small hierarchy of neutrino masses is obtained due to the different down-quark and up-quark mass hierarchies. None of the usual GUT relations between fermion masses holds exactly.Comment: 12 pages, 1 figur

Sequential random access codes and self-testing of quantum measurement instruments

Quantum Random Access Codes (QRACs) are key tools for a variety of protocols in quantum information theory. These are commonly studied in prepare-and-measure scenarios in which a sender prepares states and a receiver measures them. Here, we consider a three-party prepare-transform-measure scenario in which the simplest QRAC is implemented twice in sequence based on the same physical system. We derive optimal trade-off relations between the two QRACs. We apply our results to construct semi-device independent self-tests of quantum instruments, i.e. measurement channels with both a classical and quantum output. Finally, we show how sequential QRACs enable inference of upper and lower bounds on the sharpness parameter of a quantum instrument

Average Case ϵ-Complexity in Computer Science: A Bayesian View

Relations between average case ϵ-complexity and Bayesian statistics are discussed. An algorithm corresponds to a decision function, and the choice of information to the choice of an experiment. Adaptive information in ϵ-complexity theory corresponds to the concept of sequential experiment. Some results are reported, giving ϵ-complexity and minimax-Bayesian interpretations for factor analysis. Results from ϵ-complexity are used to establish that the optimal sequential design is no better than optimal nonsequential design for that problem

Infinite sequential Nash equilibrium

In game theory, the concept of Nash equilibrium reflects the collective stability of some individual strategies chosen by selfish agents. The concept pertains to different classes of games, e.g. the sequential games, where the agents play in turn. Two existing results are relevant here: first, all finite such games have a Nash equilibrium (w.r.t. some given preferences) iff all the given preferences are acyclic; second, all infinite such games have a Nash equilibrium, if they involve two agents who compete for victory and if the actual plays making a given agent win (and the opponent lose) form a quasi-Borel set. This article generalises these two results via a single result. More generally, under the axiomatic of Zermelo-Fraenkel plus the axiom of dependent choice (ZF+DC), it proves a transfer theorem for infinite sequential games: if all two-agent win-lose games that are built using a well-behaved class of sets have a Nash equilibrium, then all multi-agent multi-outcome games that are built using the same well-behaved class of sets have a Nash equilibrium, provided that the inverse relations of the agents' preferences are strictly well-founded.Comment: 14 pages, will be published in LMCS-2011-65

Acyclicity of Preferences, Nash Equilibria, and Subgame Perfect Equilibria: a Formal and Constructive Equivalence

In 1953, Kuhn showed that every sequential game has a Nash equilibrium by showing that a procedure, named ``backward induction'' in game theory, yields a Nash equilibrium. It actually yields Nash equilibria that define a proper subclass of Nash equilibria. In 1965, Selten named this proper subclass subgame perfect equilibria. In game theory, payoffs are rewards usually granted at the end of a game. Although traditional game theory mainly focuses on real-valued payoffs that are implicitly ordered by the usual total order over the reals, works of Simon or Blackwell already involved partially ordered payoffs. This paper generalises the notion of sequential game by replacing real-valued payoff functions with abstract atomic objects, called outcomes, and by replacing the usual total order over the reals with arbitrary binary relations over outcomes, called preferences. This introduces a general abstract formalism where Nash equilibrium, subgame perfect equilibrium, and ``backward induction'' can still be defined. This paper proves that the following three propositions are equivalent: 1) Preferences over the outcomes are acyclic. 2) Every sequential game has a Nash equilibrium. 3) Every sequential game has a subgame perfect equilibrium. The result is fully computer-certified using Coq. Beside the additional guarantee of correctness, the activity of formalisation using Coq also helps clearly identify the useful definitions and the main articulations of the proof

Universal Algorithmic Intelligence: A mathematical top->down approach

Sequential decision theory formally solves the problem of rational agents in uncertain worlds if the true environmental prior probability distribution is known. Solomonoff's theory of universal induction formally solves the problem of sequence prediction for unknown prior distribution. We combine both ideas and get a parameter-free theory of universal Artificial Intelligence. We give strong arguments that the resulting AIXI model is the most intelligent unbiased agent possible. We outline how the AIXI model can formally solve a number of problem classes, including sequence prediction, strategic games, function minimization, reinforcement and supervised learning. The major drawback of the AIXI model is that it is uncomputable. To overcome this problem, we construct a modified algorithm AIXItl that is still effectively more intelligent than any other time t and length l bounded agent. The computation time of AIXItl is of the order t x 2^l. The discussion includes formal definitions of intelligence order relations, the horizon problem and relations of the AIXI theory to other AI approaches.Comment: 70 page

A longitudinal project of new venture teamwork and outcomes

This chapter present a research project dedicated to better understand how new venture teams work together to achieve desired outcomes. Teams, as opposed to an individual, start a majority of all innovative new ventures. Yet, little research or theory exists in new venture settings about how members interact with each other over time—teamwork—to produce innovative technologies, products, and services. We believe a systematic study of social and psychological processes that underlie new venture teamwork and venture outcomes is timely and important. Unique features of our research project include: (1) a team level focus on social and psychological processes, to assess relations to proximal (e.g., innovation, first sales and team satisfaction), and distal value creation outcomes (e.g., sales growth, raised capital and profits). (2) Combined qualitative and quantitative research methodologies to provide both theory building and theory testing for the relations of interest. (3) A time-sequential design with data collection every three months over one year to allow us to investigate the relations of interest for new ventures