infinite states verification in game-theoretic logics

Many practical problems where the environment is not in the system's control such as service orchestration and contingent and multi-agent planning can be modelled in game-theoretic logics. This thesis demonstrates that the verification techniques based on regression and fixpoint approximation introduced in De Giacomo, Lesperance and Pearce [DLP10] do work on several game-theoretic problems. De Giacomo, Lesperance and Pearce [DLP10] emphasize that their study is essentially theoretical and call for complementing their work with experimental studies to understand whether these techniques are effective in practical cases. Several example problems with varying properties have been developed and, although not exhaustive nor complete,, our results nevertheless demonstrate that the techniques work on some problems. Our results show that the methods introduced in [DLP10] work for infinite domains where very few verification methods are available and allow reasoning about a wide range of game problems. Our examples also demonstrate the use of a rich language for specifying temporal properties proposed in [DLP10]. While classical model checking is well known and utilized, it is mostly restricted to finite-state models. A important aspect of the work is the demonstration of the use and effectiveness of characteristic graphs (ClaBen and Lakemeyer [CL08]) in verifying properties of games in infinite domains. A special-purpose programming language GameGolog proposed in De Giacomo, Lesperance and Pearce [DLP10] allows such game-theoretic systems to be specified procedurally at a high-level of abstraction. We show its practicality to model game structures in a convenient way that combines declarative and procedural elements. We provided examples to show the verification of GameGolog specifications using characteristic graphs. This thesis also proposes a refinement to the formalism in [DLP10] to incorporate action constraints as a mechanism to incorporate user strategies and for the modeller to supply heuristic guidance in temporal property verification. It also presents an implementation of evaluation-based fixpoint verifier that handles Situation Calculus game structures, as well as GameGolog specifications, for temporal property verification in the initial or a given situation. The verifier supports player action constraints

Dynamics of a piecewise smooth map with singularity

Experiments observing the liquid surface in a vertically oscillating container have indicated that modeling the dynamics of such systems require maps that admit states at infinity. In this paper we investigate the bifurcations in such a map. We show that though such maps in general fall in the category of piecewise smooth maps, the mechanisms of bifurcations are quite different from those in other piecewise smooth maps. We obtain the conditions of occurrence of infinite states, and show that periodic orbits containing such states are superstable. We observe period-adding cascade in this system, and obtain the scaling law of the successive periodic windows.Comment: 10 pages, 6 figures, composed in Latex2

Model checking usage policies

We study usage automata, a formal model for specifying policies on the usage of resources. Usage automata extend finite state automata with some additional features, parameters and guards, that improve their expressivity. We show that usage automata are expressive enough to model policies of real-world applications. We discuss their expressive power, and we prove that the problem of telling whether a computation complies with a usage policy is decidable. The main contribution of this paper is a model checking technique for usage automata. The model is that of usages, i.e. basic processes that describe the possible patterns of resource access and creation. In spite of the model having infinite states, because of recursion and resource creation, we devise a polynomial-time model checking technique for deciding when a usage complies with a usage policy

A Computational Framework for the Mixing Times in the QBD Processes with Infinitely-Many Levels

In this paper, we develop some matrix Poisson's equations satisfied by the mean and variance of the mixing time in an irreducible positive-recurrent discrete-time Markov chain with infinitely-many levels, and provide a computational framework for the solution to the matrix Poisson's equations by means of the UL-type of $RG$-factorization as well as the generalized inverses. In an important special case: the level-dependent QBD processes, we provide a detailed computation for the mean and variance of the mixing time. Based on this, we give new highlight on computation of the mixing time in the block-structured Markov chains with infinitely-many levels through the matrix-analytic method

Catastrophic Risks with Finite or Infinite States

Catastrophic risks are rare events with major consequences, such as market crashes, catastrophic climate change, asteroids or the extinction of a species. We show that classic expected utility theory based on Von Neumann axioms is insensitive to rare events no matter how catastrophic. Its insensitivity emerges from a requirement of continuity (e.g. Arrow's Monotone Continuity Axiom, and its relatives as defined by De Groot, Hernstein and Milnor) that anticipate average responses to extreme events. This leads to countably additive measures and `expected utility' that are insensitive to extreme risks. In a new axiomatic extension, the author (Chichilnisky 1996, 2000, 2002) requires equal treatment of rare and frequent events, deriving the new decision criterion the axioms imply. These are expected utility combined with purely finitely additive measures that focus on catastrophes, and explain the presistent observations of distributions with "fat tails" in earth sciences and financial markets. Continuity is based on the `topology of fear' introduced in Chichilnisky (2009), and is linked to Debreu's 1953 work on Adam Smith's Invisible Hand. The balance between the classic and the new axioms tests the limits of non- parametric estimation in Hilbert spaces, Chichilnisky (2008).. extending the foundations of probability & statistics (Chichilnisky 2009 and 2010) to include "black swans" or rare events, and finite as well as infinite state spaces

Catastrophic Risks with Finite or Infinite States

Catastrophic risks are rare events with major consequences, such as market crashes, catastrophic climate change, asteroids or the extinction of a species. We show that classic expected utility theory based on Von Neumann axioms is insensitive to rare events no matter how catastrophic. Its insensitivity emerges from a requirement of continuity (e.g. Arrow's Monotone Continuity Axiom, and its relatives as defined by De Groot, Hernstein and Milnor) that anticipate average responses to extreme events. This leads to countably additive measures and `expected utility' that are insensitive to extreme risks. In a new axiomatic extension, the author (Chichilnisky 1996, 2000, 2002) requires equal treatment of rare and frequent events, deriving the new decision criterion the axioms imply. These are expected utility combined with purely finitely additive measures that focus on catastrophes, and explain the presistent observations of distributions with "fat tails" in earth sciences and financial markets. Continuity is based on the `topology of fear' introduced in Chichilnisky (2009), and is linked to Debreu's 1953 work on Adam Smith's Invisible Hand. The balance between the classic and the new axioms tests the limits of non- parametric estimation in Hilbert spaces, Chichilnisky (2008).. extending the foundations of probability & statistics (Chichilnisky 2009 and 2010) to include "black swans" or rare events, and finite as well as infinite state spaces