497 research outputs found
Computability and analysis: the legacy of Alan Turing
We discuss the legacy of Alan Turing and his impact on computability and
analysis.Comment: 49 page
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
Monoidal computer III: A coalgebraic view of computability and complexity
Monoidal computer is a categorical model of intensional computation, where
many different programs correspond to the same input-output behavior. The
upshot of yet another model of computation is that a categorical formalism
should provide a much needed high level language for theory of computation,
flexible enough to allow abstracting away the low level implementation details
when they are irrelevant, or taking them into account when they are genuinely
needed. A salient feature of the approach through monoidal categories is the
formal graphical language of string diagrams, which supports visual reasoning
about programs and computations.
In the present paper, we provide a coalgebraic characterization of monoidal
computer. It turns out that the availability of interpreters and specializers,
that make a monoidal category into a monoidal computer, is equivalent with the
existence of a *universal state space*, that carries a weakly final state
machine for any pair of input and output types. Being able to program state
machines in monoidal computers allows us to represent Turing machines, to
capture their execution, count their steps, as well as, e.g., the memory cells
that they use. The coalgebraic view of monoidal computer thus provides a
convenient diagrammatic language for studying computability and complexity.Comment: 34 pages, 24 figures; in this version: added the Appendi
A discrete geometric model of concurrent program execution
A trace of the execution of a concurrent object-oriented program can be displayed in two-dimensions as a diagram of a non-metric finite geometry. The actions of a programs are represented by points, its objects and threads by vertical lines, its transactions by horizontal lines, its communications and resource sharing by sloping arrows, and its partial traces by rectangular figures. We prove informally that the geometry satisfies the laws of Concurrent Kleene Algebra (CKA); these describe and justify the interleaved implementation of multithreaded programs on computer systems with a lesser number of concurrent processors. More familiar forms of semantics (e.g., verification-oriented and operational) can be derived from CKA. Programs are represented as sets of all their possible traces of execution, and non-determinism is introduced as union of these sets. The geometry is extended to multiple levels of abstraction and granularity; a method call at a higher level can be modelled by a specification of the method body, which is implemented at a lower level. The final section describes how the axioms and definitions of the geometry have been encoded in the interactive proof tool Isabelle, and reports on progress towards automatic checking of the proofs in the paper
A Weakest Pre-Expectation Semantics for Mixed-Sign Expectations
We present a weakest-precondition-style calculus for reasoning about the
expected values (pre-expectations) of \emph{mixed-sign unbounded} random
variables after execution of a probabilistic program. The semantics of a
while-loop is well-defined as the limit of iteratively applying a functional to
a zero-element just as in the traditional weakest pre-expectation calculus,
even though a standard least fixed point argument is not applicable in this
context. A striking feature of our semantics is that it is always well-defined,
even if the expected values do not exist. We show that the calculus is sound,
allows for compositional reasoning, and present an invariant-based approach for
reasoning about pre-expectations of loops
Models of Intuitionistic Set Theory in Subtoposes of Nested Realizability Toposes
With every pca and subpca we associate the
nested realizability topos within
which we identify a class of small maps giving rise to a model of
intuitionistic set theory within . For
every subtopos of such a nested realizability topos we construct
an induced class of small maps in giving rise to
a model of intuitionistic set theory within . This covers relative
realizability toposes, modified relative realizability toposes, the modified
realizability topos and van den Berg's recent Herbrand topos
Subsumption Algorithms for Three-Valued Geometric Resolution
In our implementation of geometric resolution, the most costly operation is
subsumption testing (or matching): One has to decide for a three-valued,
geometric formula, if this formula is false in a given interpretation. The
formula contains only atoms with variables, equality, and existential
quantifiers. The interpretation contains only atoms with constants. Because the
atoms have no term structure, matching for geometric resolution is hard. We
translate the matching problem into a generalized constraint satisfaction
problem, and discuss several approaches for solving it efficiently, one direct
algorithm and two translations to propositional SAT. After that, we study
filtering techniques based on local consistency checking. Such filtering
techniques can a priori refute a large percentage of generalized constraint
satisfaction problems. Finally, we adapt the matching algorithms in such a way
that they find solutions that use a minimal subset of the interpretation. The
adaptation can be combined with every matching algorithm. The techniques
presented in this paper may have applications in constraint solving independent
of geometric resolution.Comment: This version was revised on 18.05.201
Dagstuhl News January - December 2001
"Dagstuhl News" is a publication edited especially for the members of the Foundation "Informatikzentrum Schloss Dagstuhl" to thank them for their support. The News give a summary of the scientific work being done in Dagstuhl. Each Dagstuhl Seminar is presented by a small abstract describing the contents and scientific highlights of the seminar as well as the perspectives or challenges of the research topic
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