512 research outputs found
Symbolic Algorithms for Language Equivalence and Kleene Algebra with Tests
We first propose algorithms for checking language equivalence of finite
automata over a large alphabet. We use symbolic automata, where the transition
function is compactly represented using a (multi-terminal) binary decision
diagrams (BDD). The key idea consists in computing a bisimulation by exploring
reachable pairs symbolically, so as to avoid redundancies. This idea can be
combined with already existing optimisations, and we show in particular a nice
integration with the disjoint sets forest data-structure from Hopcroft and
Karp's standard algorithm. Then we consider Kleene algebra with tests (KAT), an
algebraic theory that can be used for verification in various domains ranging
from compiler optimisation to network programming analysis. This theory is
decidable by reduction to language equivalence of automata on guarded strings,
a particular kind of automata that have exponentially large alphabets. We
propose several methods allowing to construct symbolic automata out of KAT
expressions, based either on Brzozowski's derivatives or standard automata
constructions. All in all, this results in efficient algorithms for deciding
equivalence of KAT expressions
Kleene algebra with domain
We propose Kleene algebra with domain (KAD), an extension of Kleene algebra
with two equational axioms for a domain and a codomain operation, respectively.
KAD considerably augments the expressiveness of Kleene algebra, in particular
for the specification and analysis of state transition systems. We develop the
basic calculus, discuss some related theories and present the most important
models of KAD. We demonstrate applicability by two examples: First, an
algebraic reconstruction of Noethericity and well-foundedness; second, an
algebraic reconstruction of propositional Hoare logic.Comment: 40 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
Kleene Algebra with Observations
Kleene algebra with tests (KAT) is an algebraic framework for reasoning about the control flow of sequential programs. Generalising KAT to reason about concurrent programs is not straightforward, because axioms native to KAT in conjunction with expected axioms for concurrency lead to an anomalous equation. In this paper, we propose Kleene algebra with observations (KAO), a variant of KAT, as an alternative foundation for extending KAT to a concurrent setting. We characterise the free model of KAO, and establish a decision procedure w.r.t. its equational theory
A Fast Compiler for NetKAT
High-level programming languages play a key role in a growing number of
networking platforms, streamlining application development and enabling precise
formal reasoning about network behavior. Unfortunately, current compilers only
handle "local" programs that specify behavior in terms of hop-by-hop forwarding
behavior, or modest extensions such as simple paths. To encode richer "global"
behaviors, programmers must add extra state -- something that is tricky to get
right and makes programs harder to write and maintain. Making matters worse,
existing compilers can take tens of minutes to generate the forwarding state
for the network, even on relatively small inputs. This forces programmers to
waste time working around performance issues or even revert to using
hardware-level APIs.
This paper presents a new compiler for the NetKAT language that handles rich
features including regular paths and virtual networks, and yet is several
orders of magnitude faster than previous compilers. The compiler uses symbolic
automata to calculate the extra state needed to implement "global" programs,
and an intermediate representation based on binary decision diagrams to
dramatically improve performance. We describe the design and implementation of
three essential compiler stages: from virtual programs (which specify behavior
in terms of virtual topologies) to global programs (which specify network-wide
behavior in terms of physical topologies), from global programs to local
programs (which specify behavior in terms of single-switch behavior), and from
local programs to hardware-level forwarding tables. We present results from
experiments on real-world benchmarks that quantify performance in terms of
compilation time and forwarding table size
Kleene algebra with observations
Kleene algebra with tests (KAT) is an algebraic framework for reasoning about the control flow of sequential programs. Generalising KAT to reason about concurrent programs is not straightforward, because axioms native to KAT in conjunction with expected axioms for concurrency lead to an anomalous equation. In this paper, we propose Kleene algebra with observations (KAO), a variant of KAT, as an alternative foundation for extending KAT to a concurrent setting. We characterise the free model of KAO, and establish a decision procedure w.r.t. its equational theory
Guarded Kleene algebra with tests: verification of uninterpreted programs in nearly linear time
Guarded Kleene Algebra with Tests (GKAT) is a variation on Kleene Algebra with Tests (KAT) that arises by restricting the union (+) and iteration (*) operations from KAT to predicate-guarded versions. We develop the (co)algebraic theory of GKAT and show how it can be efficiently used to reason about imperative programs. In contrast to KAT, whose equational theory is PSPACE-complete, we show that the equational theory of GKAT is (almost) linear time. We also provide a full Kleene theorem and prove completeness for an analogue of Salomaa’s axiomatization of Kleene Algebra
Decision Procedure for Synchronous Kleene Algebra
Kleene Algebra (KA) is an algebraic system that has many applications both in mathematics and
computer science. It was named after Stephen Cole Kleene who extensively studied regular
expressions and finite automata [Kle56].
Moreover it is often used to reason about programs, as it can represent sequential composition,
choice and finite iteration. Furthermore, the need to reason about actions which can be executed
concurrently, spawned SKA. SKA is an extension of KA introduced by Cristian Prisacariu
in [Pri10] that adopts a notion of concurrent actions.
Laguange equivalence is an imperishable problem in computer science. In this thesis we present
the reader with a detailed explanation of a decision procedure for SKA terms and an OCaml
implementation of said procedure as well.A Kleene Algebra (KA) é um sistema algébrico que tem bastantes aplicações quer no campo da
matemática como também da informática.
Foi batizada com o nome do seu inventor Stephen Cole Kleene, que ao longo da sua carreira fez
um estudo intensivo sobre expressões regulares e autómatos finitos [Kle56].
Quando há necessidade de raciocinar equacionalmente sobre programas, recorre-se frequentemente
à Kleene Algebra, visto que esta consegue exprimir noções de escolha, composição sequencial
e até a noção de iteração. A necessidade de raciocinar equacionalmente sobre ações
que podem ser executadas de forma concorrente levou ao aparecimento da Algebra de Kleene
Síncrona ou Synchronous Kleene Algebra (SKA). Esta última foi introduzida por Cristian Prisacariu
em 2010 no seu artigo [Pri10] como uma extensão à Kleene Algebra mas que contém uma noção
de ação concorrente.
A equivalência de linguagens é um problema perene em ciências da computação. Nesta dissertação
iremos apresentar ao leitor uma explicação detalhada de um processo de decisão para
termos de Synchronous Kleene Algebra (SKA) bem como a sua implementação utilizando a linguagem
de programação OCaml
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