858 research outputs found
Structural operational semantics for stochastic and weighted transition systems
We introduce weighted GSOS, a general syntactic framework to specify well-behaved transition systems where transitions are equipped with weights coming from a commutative monoid. We prove that weighted bisimilarity is a congruence on systems defined by weighted GSOS specifications. We illustrate the flexibility of the framework by instantiating it to handle some special cases, most notably that of stochastic transition systems. Through examples we provide weighted-GSOS definitions for common stochastic operators in the literature
Relational Foundations For Functorial Data Migration
We study the data transformation capabilities associated with schemas that
are presented by directed multi-graphs and path equations. Unlike most
approaches which treat graph-based schemas as abbreviations for relational
schemas, we treat graph-based schemas as categories. A schema is a
finitely-presented category, and the collection of all -instances forms a
category, -inst. A functor between schemas and , which can be
generated from a visual mapping between graphs, induces three adjoint data
migration functors, -inst-inst, -inst -inst, and -inst -inst. We present an algebraic query
language FQL based on these functors, prove that FQL is closed under
composition, prove that FQL can be implemented with the
select-project-product-union relational algebra (SPCU) extended with a
key-generation operation, and prove that SPCU can be implemented with FQL
Structural operational semantics for non-deterministic processes with quantitative aspects
General frameworks have been recently proposed as unifying theories for
processes combining non-determinism with quantitative aspects (such as
probabilistic or stochastically timed executions), aiming to provide general
results and tools. This paper provides two contributions in this respect.
First, we present a general GSOS specification format and a corresponding
notion of bisimulation for non-deterministic processes with quantitative
aspects. These specifications define labelled transition systems according to
the ULTraS model, an extension of the usual LTSs where the transition relation
associates any source state and transition label with state reachability weight
functions (like, e.g., probability distributions). This format, hence called
Weight Function GSOS (WF-GSOS), covers many known systems and their
bisimulations (e.g. PEPA, TIPP, PCSP) and GSOS formats (e.g. GSOS, Weighted
GSOS, Segala-GSOS, among others).
The second contribution is a characterization of these systems as coalgebras
of a class of functors, parametric on the weight structure. This result allows
us to prove soundness and completeness of the WF-GSOS specification format, and
that bisimilarities induced by these specifications are always congruences.Comment: Extended version of arXiv:1406.206
TOWARDS MODELS OF REALISTIC COMPUTING MACHINES IN COMPUTER SCIENCE
The paper presents an approach to system modelling in design of both hardware and software systems. It is based on the definition of models of machines that can be directly implemented. The paper shows how to render less abstract and more realistic the abstract machines defined by theoreticians, so that they can capture implementation and technological-oriented aspects, such as testability, and allow an easy transition to final implementations. A realistic abstract machine for lambda-calculus is then presented and the design of system for lambda-expressions evaluation is illustrated. The architecture chosen for the system is based on a collection of finite state automata, evolving concurrently and communicating via a broadcast system. Some conclusive remarks about the
use of realistic models arc finally drawn
On partial order semantics for SAT/SMT-based symbolic encodings of weak memory concurrency
Concurrent systems are notoriously difficult to analyze, and technological
advances such as weak memory architectures greatly compound this problem. This
has renewed interest in partial order semantics as a theoretical foundation for
formal verification techniques. Among these, symbolic techniques have been
shown to be particularly effective at finding concurrency-related bugs because
they can leverage highly optimized decision procedures such as SAT/SMT solvers.
This paper gives new fundamental results on partial order semantics for
SAT/SMT-based symbolic encodings of weak memory concurrency. In particular, we
give the theoretical basis for a decision procedure that can handle a fragment
of concurrent programs endowed with least fixed point operators. In addition,
we show that a certain partial order semantics of relaxed sequential
consistency is equivalent to the conjunction of three extensively studied weak
memory axioms by Alglave et al. An important consequence of this equivalence is
an asymptotically smaller symbolic encoding for bounded model checking which
has only a quadratic number of partial order constraints compared to the
state-of-the-art cubic-size encoding.Comment: 15 pages, 3 figure
Coinduction up to in a fibrational setting
Bisimulation up-to enhances the coinductive proof method for bisimilarity,
providing efficient proof techniques for checking properties of different kinds
of systems. We prove the soundness of such techniques in a fibrational setting,
building on the seminal work of Hermida and Jacobs. This allows us to
systematically obtain up-to techniques not only for bisimilarity but for a
large class of coinductive predicates modelled as coalgebras. By tuning the
parameters of our framework, we obtain novel techniques for unary predicates
and nominal automata, a variant of the GSOS rule format for similarity, and a
new categorical treatment of weak bisimilarity
Combinatorial Species and Labelled Structures
The theory of combinatorial species was developed in
the 1980s as part of the mathematical subfield of enumerative
combinatorics, unifying and putting on a firmer theoretical basis a
collection of techniques centered around generating
functions. The theory of algebraic data
types was developed, around the same time, in functional
programming languages such as Hope and Miranda, and is still used
today in languages such as Haskell, the ML family, and Scala. Despite
their disparate origins, the two theories have striking
similarities. In particular, both constitute algebraic frameworks in
which to construct structures of interest. Though the similarity has
not gone unnoticed, a link between combinatorial species and algebraic
data types has never been systematically explored. This dissertation
lays the theoretical groundwork for a preciseâand, hopefully,
usefulâbridge bewteen the two theories. One of the key
contributions is to port the theory of species from a classical,
untyped set theory to a constructive type theory. This porting process
is nontrivial, and involves fundamental issues related to equality and
finiteness; the recently developed homotopy type
theory is put to good use formalizing these issues in a
satisfactory way. In conjunction with this port, species as general
functor categories are considered, systematically analyzing the
categorical properties necessary to define each standard species
operation. Another key contribution is to clarify the role of species
as labelled shapes, not containing any data, and to
use the theory of analytic functors to model labelled
data structures, which have both labelled shapes and data associated
to the labels. Finally, some novel species variants are considered,
which may prove to be of use in explicitly modelling the memory layout
used to store labelled data structures
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