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Which Classes of Origin Graphs Are Generated by Transducers.
We study various models of transducers equipped with origin information. We consider the semantics of these models as particular graphs, called origin graphs, and we characterise the families of such graphs recognised by streaming string transducers
Caterpillar dualities and regular languages
We characterize obstruction sets in caterpillar dualities in terms of regular
languages, and give a construction of the dual of a regular family of
caterpillars. We show that these duals correspond to the constraint
satisfaction problems definable by a monadic linear Datalog program with at
most one EDB per rule
Bicategorical Semantics for Nondeterministic Computation
We outline a bicategorical syntax for the interaction between public and
private information in classical information theory. We use this to give
high-level graphical definitions of encrypted communication and secret sharing
protocols, including a characterization of their security properties.
Remarkably, this makes it clear that the protocols have an identical abstract
form to the quantum teleportation and dense coding procedures, yielding
evidence of a deep connection between classical and quantum information
processing. We also formulate public-key cryptography using our scheme.
Specific implementations of these protocols as nondeterministic classical
procedures are recovered by applying our formalism in a symmetric monoidal
bicategory of matrices of relations.Comment: 21 page
Descriptive Complexity of Deterministic Polylogarithmic Time and Space
We propose logical characterizations of problems solvable in deterministic
polylogarithmic time (PolylogTime) and polylogarithmic space (PolylogSpace). We
introduce a novel two-sorted logic that separates the elements of the input
domain from the bit positions needed to address these elements. We prove that
the inflationary and partial fixed point vartiants of this logic capture
PolylogTime and PolylogSpace, respectively. In the course of proving that our
logic indeed captures PolylogTime on finite ordered structures, we introduce a
variant of random-access Turing machines that can access the relations and
functions of a structure directly. We investigate whether an explicit predicate
for the ordering of the domain is needed in our PolylogTime logic. Finally, we
present the open problem of finding an exact characterization of
order-invariant queries in PolylogTime.Comment: Submitted to the Journal of Computer and System Science
Probabilistic Rely-guarantee Calculus
Jones' rely-guarantee calculus for shared variable concurrency is extended to
include probabilistic behaviours. We use an algebraic approach which combines
and adapts probabilistic Kleene algebras with concurrent Kleene algebra.
Soundness of the algebra is shown relative to a general probabilistic event
structure semantics. The main contribution of this paper is a collection of
rely-guarantee rules built on top of that semantics. In particular, we show how
to obtain bounds on probabilities by deriving rely-guarantee rules within the
true-concurrent denotational semantics. The use of these rules is illustrated
by a detailed verification of a simple probabilistic concurrent program: a
faulty Eratosthenes sieve.Comment: Preprint submitted to TCS-QAP
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