649 research outputs found
Grammatical structures and logical deductions
The three essays presented here concern natural connections between grammatical derivations and structures provided by certain standard grammar formalisms, on the one hand, and deductions in logical systems, on the other hand. In the first essay we analyse the adequacy of Polish notation for higher-order languages. The Ajdukiewicz algorithm (Ajdukiewicz 1935) is discussed in terms of generalized MP-deductions. We exhibit a failure in Ajdukiewicz’s original version of the algorithm and give a correct one; we prove that generalized MP-deductions have the frontier property, which is essential for the plausibility of Polish notation. The second essay deals with logical systems corresponding to different grammar formalisms, as e.g. Finite State Acceptors, Context-Free Grammars, Categorial Grammars, and others. We show how can logical methods be used to establish certain linguistically significant properties of formal grammars. The third essay discusses the interplay between Natural Deduction proofs in grammar oriented logics and semantic structures expressible by typed lambda terms and combinators
Bell's Theorem, Many Worlds and Backwards-Time Physics: Not Just a Matter of Interpretation
The classic "Bell's Theorem" of Clauser, Holt, Shimony and Horne tells us
that we must give up at least one of: (1) objective reality (aka "hidden
variables"); (2) locality; or (3) time-forwards macroscopic statistics (aka
"causality"). The orthodox Copenhagen version of physics gives up the first.
The many-worlds theory of Everett and Wheeler gives up the second. The
backwards-time theory of physics (BTP) gives up the third. Contrary to
conventional wisdom, empirical evidence strongly favors Everett-Wheeler over
orthodox Copenhagen. BTP has two major variations -- a many-worlds version, and
a neoclassical version of partial differential equations (PDE) in the spirit of
Einstein. Section 2 discusses quantum measurement according to BTP, focusing on
how we represent condensed matter objects like polarizers in a Bell's Theorem
experiment or in tests of Hawking's cosmology. The Backwards Time Telegraph,
though speculative, is discussed.Comment: 15 pages, 29 refs, 2 figures, 11 equations. Revision adds brief
appendix on opto-electronic circuit design issues to detect or exploit
backwards time effect
Applying Formal Methods to Networking: Theory, Techniques and Applications
Despite its great importance, modern network infrastructure is remarkable for
the lack of rigor in its engineering. The Internet which began as a research
experiment was never designed to handle the users and applications it hosts
today. The lack of formalization of the Internet architecture meant limited
abstractions and modularity, especially for the control and management planes,
thus requiring for every new need a new protocol built from scratch. This led
to an unwieldy ossified Internet architecture resistant to any attempts at
formal verification, and an Internet culture where expediency and pragmatism
are favored over formal correctness. Fortunately, recent work in the space of
clean slate Internet design---especially, the software defined networking (SDN)
paradigm---offers the Internet community another chance to develop the right
kind of architecture and abstractions. This has also led to a great resurgence
in interest of applying formal methods to specification, verification, and
synthesis of networking protocols and applications. In this paper, we present a
self-contained tutorial of the formidable amount of work that has been done in
formal methods, and present a survey of its applications to networking.Comment: 30 pages, submitted to IEEE Communications Surveys and Tutorial
Security of Quantum Key Distribution
We propose various new techniques in quantum information theory, including a
de Finetti style representation theorem for finite symmetric quantum states. As
an application, we give a proof for the security of quantum key distribution
which applies to arbitrary protocols.Comment: PhD thesis; index adde
A categorical semantics for causal structure
We present a categorical construction for modelling causal structures within
a general class of process theories that include the theory of classical
probabilistic processes as well as quantum theory. Unlike prior constructions
within categorical quantum mechanics, the objects of this theory encode
fine-grained causal relationships between subsystems and give a new method for
expressing and deriving consequences for a broad class of causal structures. We
show that this framework enables one to define families of processes which are
consistent with arbitrary acyclic causal orderings. In particular, one can
define one-way signalling (a.k.a. semi-causal) processes, non-signalling
processes, and quantum -combs. Furthermore, our framework is general enough
to accommodate recently-proposed generalisations of classical and quantum
theory where processes only need to have a fixed causal ordering locally, but
globally allow indefinite causal ordering.
To illustrate this point, we show that certain processes of this kind, such
as the quantum switch, the process matrices of Oreshkov, Costa, and Brukner,
and a classical three-party example due to Baumeler, Feix, and Wolf are all
instances of a certain family of processes we refer to as in
the appropriate category of higher-order causal processes. After defining these
families of causal structures within our framework, we give derivations of
their operational behaviour using simple, diagrammatic axioms.Comment: Extended version of a LICS 2017 paper with the same titl
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