435,875 research outputs found
A Type- and Control-Flow Analysis for System F: Technical Report
We present a monovariant flow analysis for System F (with recursion). The flow analysis yields both control-flow information, approximating the λ- and Λ-expressions that may be bound to variables, and type-flow information, approximating the type expressions that may instantiate type variables. Moreover, the two flows are mutually beneficial: the control flow determines which Λ-expressions may be applied to which type expressions (and, hence, which type expressions may instantiate which type variables), while the type flow filters the λ- and Λ-expressions that may be bound to variables (by rejecting expressions with static types that are incompatible with the static type of the variable under the type flow). As is typical for a monovariant control-flow analysis, control-flow information is expressed as an abstract environment mapping variables to sets of (syntactic) λ- and Λ-expressions that occur in the program under analysis. Similarly, type-flow information is expressed as an abstract environment mapping type variables to sets of (syntactic) types that occur in the program under analysis. Compatibility of static types (with free type variables) under a type flow is decided by interpreting the abstract environment as productions for a regular-tree grammar and querying if the languages generated by taking the types in question as starting terms have a non-empty intersection. This is a companion technical report, providing additional commentary and proof details, to a paper [11] appearing in Implementation and Application of Functional Languages: 24th International Symposium (IFL’12)
Exactly solvable model of A + A \to 0 reactions on a heterogeneous catalytic chain
We present an exact solution describing equilibrium properties of the
catalytically-activated A + A \to 0 reaction taking place on a one-dimensional
lattice, where some of the sites possess special "catalytic" properties. The A
particles undergo continuous exchanges with the vapor phase; two neighboring
adsorbed As react when at least one of them resides on a catalytic site (CS).
We consider three situations for the CS distribution: regular, annealed random
and quenched random. For all three CS distribution types, we derive exact
results for the disorder-averaged pressure and present exact asymptotic
expressions for the particles' mean density. The model studied here furnishes
another example of a 1D Ising-type system with random multi-site interactions
which admits an exact solution.Comment: 7 pages, 3 Figures, appearing in Europhysics Letter
Regular Expression Types for XML
We propose regular expression types as a foundation for statically typed XML processing languages. Regular expression types, like most schema languages for XML, introduce regular expression notations such as repetition (*), alternation (|), etc., to describe XML documents. The novelty of our type system is a semantic presentation of subtyping, as inclusion between the sets of documents denoted by two types. We give several examples illustrating the usefulness of this form of subtyping in XML processing.
The decision problem for the subtype relation reduces to the inclusion problem between tree automata, which is known to be EXPTIME-complete. To avoid this high complexity in typical cases, we develop a practical algorithm that, unlike classical algorithms based on determinization of tree automata, checks the inclusion relation by a top-down traversal of the original type expressions. The main advantage of this algorithm is that it can exploit the property that type expressions being compared often share portions of their representations. Our algorithm is a variant of Aiken and Murphy\u27s set-inclusion constraint solver, to which are added several new implementation techniques, correctness proofs, and preliminary performance measurements on some small programs in the domain of typed XML processing
Image Reflection on Process Graphs -- A Novel Approach for the Completeness of an Axiomatization of 1-Free Regular Expressions Modulo Bisimilarity
We analyze a phenomenon called ``image reflection'' on a type of
characterization graphs -- LLEE charts -- of 1-free regular expressions. Due to
the correspondence between 1-free regular expressions and the provable
solutions of LEE/LLEE charts, this observation naturally leads to a new proof
for the completeness of the proof system \MilIfree\ for 1-free regular
expressions modulo bisimulation equivalence. The critical part of the previous
proof is to show that bisimulation collapse, which plays the role in linking
the provable solutions of two LLEE charts, is still an LLEE chart. The
difference of our proof, compared to the previous one, is that we do not rely
on the graph transformations from LLEE charts into their bisimulation collapses
by merging two carefully-selected bisimilar nodes in each transformation step.
Instead, we directly show that the bisimulation collapse of an LLEE chart
possesses an LEE/LLEE structure based on its set of images mapped through the
bisimulation function from the LLEE chart, and the constrained relation between
the images and their so-called ``well-structured'' looping-back charts
pre-images on the LLEE chart. Our approach provides a novel angle to look at
this problem and related problems, and can also be used for simplifying the
graph transformations in the proof of the completeness problem of the proof
system \Mil\ for regular expressions modulo bisimulation equivalence, which had
remained open until very recently.Comment: Minor typos and further polishing from the reviewers' comments of the
conference that rejected u
Mutation of Directed Graphs -- Corresponding Regular Expressions and Complexity of Their Generation
Directed graphs (DG), interpreted as state transition diagrams, are
traditionally used to represent finite-state automata (FSA). In the context of
formal languages, both FSA and regular expressions (RE) are equivalent in that
they accept and generate, respectively, type-3 (regular) languages. Based on
our previous work, this paper analyzes effects of graph manipulations on
corresponding RE. In this present, starting stage we assume that the DG under
consideration contains no cycles. Graph manipulation is performed by deleting
or inserting of nodes or arcs. Combined and/or multiple application of these
basic operators enable a great variety of transformations of DG (and
corresponding RE) that can be seen as mutants of the original DG (and
corresponding RE). DG are popular for modeling complex systems; however they
easily become intractable if the system under consideration is complex and/or
large. In such situations, we propose to switch to corresponding RE in order to
benefit from their compact format for modeling and algebraic operations for
analysis. The results of the study are of great potential interest to mutation
testing
A Typed Calculus for Querying Distributed XML Documents
We study the problems related to querying large, distributed XML documents. Our proposal takes the form of a new process calculus in which XML data are processes that can be queried by means of concurrent pattern-matching expressions. What we achieve is a functional, strongly-typed programming model based on three main ingredients: an asynchronous process calculus in the style of Milner's pi-calculus and existing semantics for concurrent-ML; a model where documents and expressions are both represented as processes, and where evaluation is represented as a parallel composition of the two; a static type system based on regular expression types
Session Coalgebras: A Coalgebraic View on Regular and Context-Free Session Types
Compositional methods are central to the verification of software systems. For concurrent and communicating systems, compositional techniques based on behavioural type systems have received much attention. By abstracting communication protocols as types, these type systems can statically check that channels in a program interact following a certain protocol—whether messages are exchanged in the intended order. In this article, we put on our coalgebraic spectacles to investigate session types, a widely studied class of behavioural type systems. We provide a syntax-free description of session-based concurrency as states of coalgebras. As a result, we rediscover type equivalence, duality, and subtyping relations in terms of canonical coinductive presentations. In turn, this coinductive presentation enables us to derive a decidable type system with subtyping for the π-calculus, in which the states of a coalgebra will serve as channel protocols. Going full circle, we exhibit a coalgebra structure on an existing session type system, and show that the relations and type system resulting from our coalgebraic perspective coincide with existing ones. We further apply to session coalgebras the coalgebraic approach to regular languages via the so-called rational fixed point, inspired by the trinity of automata, regular languages, and regular expressions with session coalgebras, rational fixed point, and session types, respectively. We establish a suitable restriction on session coalgebras that determines a similar trinity, and reveals the mismatch between usual session types and our syntax-free coalgebraic approach. Furthermore, we extend our coalgebraic approach to account for context-free session types, by equipping session coalgebras with a stack
Edge effects in graphene nanostructures: I. From multiple reflection expansion to density of states
We study the influence of different edge types on the electronic density of
states of graphene nanostructures. To this end we develop an exact expansion
for the single particle Green's function of ballistic graphene structures in
terms of multiple reflections from the system boundary, that allows for a
natural treatment of edge effects. We first apply this formalism to calculate
the average density of states of graphene billiards. While the leading term in
the corresponding Weyl expansion is proportional to the billiard area, we find
that the contribution that usually scales with the total length of the system
boundary differs significantly from what one finds in semiconductor-based,
Schr\"odinger type billiards: The latter term vanishes for armchair and
infinite mass edges and is proportional to the zigzag edge length, highlighting
the prominent role of zigzag edges in graphene. We then compute analytical
expressions for the density of states oscillations and energy levels within a
trajectory based semiclassical approach. We derive a Dirac version of
Gutzwiller's trace formula for classically chaotic graphene billiards and
further obtain semiclassical trace formulae for the density of states
oscillations in regular graphene cavities. We find that edge dependent
interference of pseudospins in graphene crucially affects the quantum spectrum.Comment: to be published in Phys. Rev.
- …