3,333 research outputs found
An Open Challenge Problem Repository for Systems Supporting Binders
A variety of logical frameworks support the use of higher-order abstract
syntax in representing formal systems; however, each system has its own set of
benchmarks. Even worse, general proof assistants that provide special libraries
for dealing with binders offer a very limited evaluation of such libraries, and
the examples given often do not exercise and stress-test key aspects that arise
in the presence of binders. In this paper we design an open repository ORBI
(Open challenge problem Repository for systems supporting reasoning with
BInders). We believe the field of reasoning about languages with binders has
matured, and a common set of benchmarks provides an important basis for
evaluation and qualitative comparison of different systems and libraries that
support binders, and it will help to advance the field.Comment: In Proceedings LFMTP 2015, arXiv:1507.0759
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
Matching Logic
This paper presents matching logic, a first-order logic (FOL) variant for
specifying and reasoning about structure by means of patterns and pattern
matching. Its sentences, the patterns, are constructed using variables,
symbols, connectives and quantifiers, but no difference is made between
function and predicate symbols. In models, a pattern evaluates into a power-set
domain (the set of values that match it), in contrast to FOL where functions
and predicates map into a regular domain. Matching logic uniformly generalizes
several logical frameworks important for program analysis, such as:
propositional logic, algebraic specification, FOL with equality, modal logic,
and separation logic. Patterns can specify separation requirements at any level
in any program configuration, not only in the heaps or stores, without any
special logical constructs for that: the very nature of pattern matching is
that if two structures are matched as part of a pattern, then they can only be
spatially separated. Like FOL, matching logic can also be translated into pure
predicate logic with equality, at the same time admitting its own sound and
complete proof system. A practical aspect of matching logic is that FOL
reasoning with equality remains sound, so off-the-shelf provers and SMT solvers
can be used for matching logic reasoning. Matching logic is particularly
well-suited for reasoning about programs in programming languages that have an
operational semantics, but it is not limited to this
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
Characterizing specification languages which admit initial semantics
AbstractThe paper proposes an axiomatic approach to specification languages, and introduces notions of reducibility and equivalence as tools for their study and comparison. Algebraic specification languages are characterized up to equivalence. They are shown to be limited in expressive power by implicational languages
Combining Algebraic and Set-Theoretic Specifications (Extended Version)
Specification frameworks such as B and Z provide power sets and cartesianproducts as built-in type constructors, and employ a rich notation fordefining (among other things) abstract data types using formulae of predicatelogic and lambda-notation. In contrast, the so-called algebraic specification frameworks often limit the type structure to sort constants andfirst-order functionalities, and restrict formulae to (conditional) equations.Here, we propose an intermediate framework where algebraic specificationsare enriched with a set-theoretic type structure, but formulae remain in thelogic of equational Horn clauses. This combines an expressive yet modestspecification notation with simple semantics and tractable proof theory
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