Continuous Time and Consistent Histories

We discuss the use of histories labelled by a continuous time in the approach to consistent-histories quantum theory in which propositions about the history of the system are represented by projection operators on a Hilbert space. This extends earlier work by two of us \cite{IL95} where we showed how a continuous time parameter leads to a history algebra that is isomorphic to the canonical algebra of a quantum field theory. We describe how the appropriate representation of the history algebra may be chosen by requiring the existence of projection operators that represent propositions about time average of the energy. We also show that the history description of quantum mechanics contains an operator corresponding to velocity that is quite distinct from the momentum operator. Finally, the discussion is extended to give a preliminary account of quantum field theory in this approach to the consistent histories formalism.Comment: Typeset in RevTe

A framework for automated concurrency verification

Reasoning systems based on Concurrent Separation Logic make verifying complex concurrent algorithms readily possible. Such algorithms contain subtle protocols of permission and resource transfer between threads; to cope with these intricacies, modern concurrent separation logics contain many moving parts and integrate many bespoke logical components. Verifying concurrent algorithms by hand consumes much time, effort, and expertise. As a result, computer-assisted verification is a fertile research topic, and fully automated verification is a popular research goal. Unfortunately, the complexity of modern concurrent separation logics makes them hard to automate, and the proliferation and fast turnover of such logics causes a downward pressure against building tools for new logics. As a result, many such logics lack tooling. This dissertation proposes Starling: a scheme for creating concurrent program logics that are automatable by construction. Starling adapts the existing Concurrent Views Framework for sound concurrent reasoning systems, overlaying a framework for reducing concurrent proof outlines to verification conditions in existing theories (such as those accepted by off-the-shelf sequential solvers). This dissertation describes Starling in a bottom-up, modular manner. First, it shows the derivation of a series of general concurrency proof rules from the Views framework. Next, it shows how one such rule leads to the Starling framework itself. From there, it outlines a series of increasingly elaborate frontends: ways of decomposing individual Hoare triples over atomic actions into verification conditions suitable for encoding into backend theories. Each frontend leads to a concurrent program logic. Finally, the dissertation presents a tool for verifying C-style concurrent proof outlines, based on one of the above frontends. It gives examples of such outlines, covering a variety of algorithms, backend solvers, and proof techniques

The Complexity of Model Checking Higher-Order Fixpoint Logic

Higher-Order Fixpoint Logic (HFL) is a hybrid of the simply typed \lambda-calculus and the modal \lambda-calculus. This makes it a highly expressive temporal logic that is capable of expressing various interesting correctness properties of programs that are not expressible in the modal \lambda-calculus. This paper provides complexity results for its model checking problem. In particular we consider those fragments of HFL built by using only types of bounded order k and arity m. We establish k-fold exponential time completeness for model checking each such fragment. For the upper bound we use fixpoint elimination to obtain reachability games that are singly-exponential in the size of the formula and k-fold exponential in the size of the underlying transition system. These games can be solved in deterministic linear time. As a simple consequence, we obtain an exponential time upper bound on the expression complexity of each such fragment. The lower bound is established by a reduction from the word problem for alternating (k-1)-fold exponential space bounded Turing Machines. Since there are fixed machines of that type whose word problems are already hard with respect to k-fold exponential time, we obtain, as a corollary, k-fold exponential time completeness for the data complexity of our fragments of HFL, provided m exceeds 3. This also yields a hierarchy result in expressive power.Comment: 33 pages, 2 figures, to be published in Logical Methods in Computer Scienc

What room for viewpoints?

http://www.cssp.cnrs.fr/eiss6/jayez-eiss6.pd

Logic and the Foundations of Game and Decision Theory (LOFT 7)

This volume collects together revised papers originally presented at the 7th Conference on Logic and the Foundations of Game and Decision Theory (LOFT 2006). LOFT is a key venue for presenting research at the intersection of logic, economics and computer science, and the present collection gives a lively and wide-ranging view of an exciting and rapidly growing area

Verification of temporal-epistemic properties of access control systems

Verification of access control systems against vulnerabilities has always been a challenging problem in the world of computer security. The complication of security policies in large- scale multi-agent systems increases the possible existence of vulnerabilities as a result of mistakes in policy definition. This thesis explores automated methods in order to verify temporal and epistemic properties of access control systems. While temporal property verification can reveal a considerable number of security holes, verification of epistemic properties in multi-agent systems enable us to infer about agents' knowledge in the system and hence, to detect unauthorized information flow. This thesis first presents a framework for knowledge-based verification of dynamic access control policies. This framework models a coalition-based system, which evaluates if a property or a goal can be achieved by a coalition of agents restricted by a set of permissions defined in the policy. Knowledge is restricted to the information that agents can acquire by reading system information in order to increase time and memory efficiency. The framework has its own model-checking method and is implemented in Java and released as an open source tool named \char{cmmi10}{0x50}\char{cmmi10}{0x6f}\char{cmmi10}{0x6c}\char{cmmi10}{0x69}\char{cmmi10}{0x56}\char{cmmi10}{0x65}\char{cmmi10}{0x72}. In order to detect information leakage as a result of reasoning, the second part of this thesis presents a complimentary technique that evaluates access control policies over temporal-epistemic properties where the knowledge is gained by reasoning. We will demonstrate several case studies for a subset of properties that deal with reasoning about knowledge. To increase the efficiency, we develop an automated abstraction refinement technique for evaluating temporal-epistemic properties. For the last part of the thesis, we develop a sound and complete algorithm in order to identify information leakage in Datalog-based trust management systems

On the Consistent Histories Approach to Quantum Mechanics

We review the consistent histories formulations of quantum mechanics developed by Griffiths, Omn\`es and Gell-Mann and Hartle, and describe the classification of consistent sets. We illustrate some general features of consistent sets by a few simple lemmas and examples. We consider various interpretations of the formalism, and examine the new problems which arise in reconstructing the past and predicting the future. It is shown that Omn\`es' characterisation of true statements --- statements which can be deduced unconditionally in his interpretation --- is incorrect. We examine critically Gell-Mann and Hartle's interpretation of the formalism, and in particular their discussions of communication, prediction and retrodiction, and conclude that their explanation of the apparent persistence of quasiclassicality relies on assumptions about an as yet unknown theory of experience. Our overall conclusion is that the consistent histories approach illustrates the need to supplement quantum mechanics by some selection principle in order to produce a fundamental theory capable of unconditional predictions.Comment: Published version, to appear in J. Stat. Phys. in early 1996. The main arguments and conclusions remain unaltered, but there are significant revisions from the earlier archive version. These include a new subsection on interpretations of the formalism, other additions clarifying various arguments in response to comments, and some minor corrections. (87 pages, TeX with harvmac.