18,365 research outputs found
An Algebra of Hierarchical Graphs and its Application to Structural Encoding
We define an algebraic theory of hierarchical graphs, whose axioms
characterise graph isomorphism: two terms are equated exactly when
they represent the same graph. Our algebra can be understood as
a high-level language for describing graphs with a node-sharing, embedding
structure, and it is then well suited for defining graphical
representations of software models where nesting and linking are key
aspects. In particular, we propose the use of our graph formalism as a
convenient way to describe configurations in process calculi equipped
with inherently hierarchical features such as sessions, locations, transactions,
membranes or ambients. The graph syntax can be seen as an
intermediate representation language, that facilitates the encodings of
algebraic specifications, since it provides primitives for nesting, name
restriction and parallel composition. In addition, proving soundness
and correctness of an encoding (i.e. proving that structurally equivalent
processes are mapped to isomorphic graphs) becomes easier as it can
be done by induction over the graph syntax
On Role Logic
We present role logic, a notation for describing properties of relational
structures in shape analysis, databases, and knowledge bases. We construct role
logic using the ideas of de Bruijn's notation for lambda calculus, an encoding
of first-order logic in lambda calculus, and a simple rule for implicit
arguments of unary and binary predicates. The unrestricted version of role
logic has the expressive power of first-order logic with transitive closure.
Using a syntactic restriction on role logic formulas, we identify a natural
fragment RL^2 of role logic. We show that the RL^2 fragment has the same
expressive power as two-variable logic with counting C^2 and is therefore
decidable. We present a translation of an imperative language into the
decidable fragment RL^2, which allows compositional verification of programs
that manipulate relational structures. In addition, we show how RL^2 encodes
boolean shape analysis constraints and an expressive description logic.Comment: 20 pages. Our later SAS 2004 result builds on this wor
Relational type-checking for MELL proof-structures. Part 1: Multiplicatives
Relational semantics for linear logic is a form of non-idempotent
intersection type system, from which several informations on the execution of a
proof-structure can be recovered. An element of the relational interpretation
of a proof-structure R with conclusion acts thus as a type (refining
) having R as an inhabitant. We are interested in the following
type-checking question: given a proof-structure R, a list of formulae ,
and a point x in the relational interpretation of , is x in the
interpretation of R? This question is decidable. We present here an algorithm
that decides it in time linear in the size of R, if R is a proof-structure in
the multiplicative fragment of linear logic. This algorithm can be extended to
larger fragments of multiplicative-exponential linear logic containing
-calculus
On Unification Modulo One-Sided Distributivity: Algorithms, Variants and Asymmetry
An algorithm for unification modulo one-sided distributivity is an early
result by Tid\'en and Arnborg. More recently this theory has been of interest
in cryptographic protocol analysis due to the fact that many cryptographic
operators satisfy this property. Unfortunately the algorithm presented in the
paper, although correct, has recently been shown not to be polynomial time
bounded as claimed. In addition, for some instances, there exist most general
unifiers that are exponentially large with respect to the input size. In this
paper we first present a new polynomial time algorithm that solves the decision
problem for a non-trivial subcase, based on a typed theory, of unification
modulo one-sided distributivity. Next we present a new polynomial algorithm
that solves the decision problem for unification modulo one-sided
distributivity. A construction, employing string compression, is used to
achieve the polynomial bound. Lastly, we examine the one-sided distributivity
problem in the new asymmetric unification paradigm. We give the first
asymmetric unification algorithm for one-sided distributivity
A Typed Model for Linked Data
The term Linked Data is used to describe ubiquitous and emerging semi-structured data formats on the Web. URIs in Linked Data allow diverse data sources to link to each other, forming a Web of Data. A calculus which models concurrent queries and updates over Linked Data is presented. The calculus exhibits operations essential for declaring rich atomic actions. The operations recover emergent structure in the loosely structured Web of Data. The calculus is executable due to its operational semantics. A light type system ensures that URIs with a distinguished role are used consistently. The main theorem verifies that the light type system and operational semantics work at the same level of granularity, so are compatible. Examples show that a range of existing and emerging standards are captured. Data formats include RDF, named graphs and feeds. The primitives of the calculus model SPARQL Query and the Atom Publishing Protocol. The subtype system is based on RDFS, which improves interoperability. Examples focuss on the SPARQL Update proposal for which a fine grained operational semantics is developed. Further potential high level languages are outlined for exploiting Linked Data
Transforming specifications of observable behaviour into programs
A methodology for deriving programs from specifications of observable
behaviour is described. The class of processes to which this methodology
is applicable includes those whose state changes are fully definable by labelled
transition systems, for example communicating processes without
internal state changes. A logic program representation of such labelled
transition systems is proposed, interpreters based on path searching techniques
are defined, and the use of partial evaluation techniques to derive
the executable programs is described
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