8,857 research outputs found
Partially-commutative context-free languages
The paper is about a class of languages that extends context-free languages
(CFL) and is stable under shuffle. Specifically, we investigate the class of
partially-commutative context-free languages (PCCFL), where non-terminal
symbols are commutative according to a binary independence relation, very much
like in trace theory. The class has been recently proposed as a robust class
subsuming CFL and commutative CFL. This paper surveys properties of PCCFL. We
identify a natural corresponding automaton model: stateless multi-pushdown
automata. We show stability of the class under natural operations, including
homomorphic images and shuffle. Finally, we relate expressiveness of PCCFL to
two other relevant classes: CFL extended with shuffle and trace-closures of
CFL. Among technical contributions of the paper are pumping lemmas, as an
elegant completion of known pumping properties of regular languages, CFL and
commutative CFL.Comment: In Proceedings EXPRESS/SOS 2012, arXiv:1208.244
Safety verification of asynchronous pushdown systems with shaped stacks
In this paper, we study the program-point reachability problem of concurrent
pushdown systems that communicate via unbounded and unordered message buffers.
Our goal is to relax the common restriction that messages can only be retrieved
by a pushdown process when its stack is empty. We use the notion of partially
commutative context-free grammars to describe a new class of asynchronously
communicating pushdown systems with a mild shape constraint on the stacks for
which the program-point coverability problem remains decidable. Stacks that fit
the shape constraint may reach arbitrary heights; further a process may execute
any communication action (be it process creation, message send or retrieval)
whether or not its stack is empty. This class extends previous computational
models studied in the context of asynchronous programs, and enables the safety
verification of a large class of message passing programs
Non-normal modalities in variants of Linear Logic
This article presents modal versions of resource-conscious logics. We
concentrate on extensions of variants of Linear Logic with one minimal
non-normal modality. In earlier work, where we investigated agency in
multi-agent systems, we have shown that the results scale up to logics with
multiple non-minimal modalities. Here, we start with the language of
propositional intuitionistic Linear Logic without the additive disjunction, to
which we add a modality. We provide an interpretation of this language on a
class of Kripke resource models extended with a neighbourhood function: modal
Kripke resource models. We propose a Hilbert-style axiomatization and a
Gentzen-style sequent calculus. We show that the proof theories are sound and
complete with respect to the class of modal Kripke resource models. We show
that the sequent calculus admits cut elimination and that proof-search is in
PSPACE. We then show how to extend the results when non-commutative connectives
are added to the language. Finally, we put the logical framework to use by
instantiating it as logics of agency. In particular, we propose a logic to
reason about the resource-sensitive use of artefacts and illustrate it with a
variety of examples
-Gaussian processes: non-commutative and classical aspects
We examine, for , -Gaussian processes, i.e. families of operators
(non-commutative random variables) -- where the fulfill
the -commutation relations a_sa_t^*-qa_t^*a_s=c(s,t)\cdot \id for some
covariance function -- equipped with the vacuum expectation
state. We show that there is a -analogue of the Gaussian functor of second
quantization behind these processes and that this structure can be used to
translate questions on -Gaussian processes into corresponding (and much
simpler) questions in the underlying Hilbert space. In particular, we use this
idea to show that a large class of -Gaussian processes possess a
non-commutative kind of Markov property, which ensures that there exist
classical versions of these non-commutative processes. This answers an old
question of Frisch and Bourret \cite{FB}.Comment: AMS-TeX 2.
Categorical Ontology of Complex Systems, Meta-Systems and Theory of Levels: The Emergence of Life, Human Consciousness and Society
Single cell interactomics in simpler organisms, as well as somatic cell interactomics in multicellular organisms, involve biomolecular interactions in complex signalling pathways that were recently represented in modular terms by quantum automata with ‘reversible behavior’ representing normal cell cycling and division. Other implications of such quantum automata, modular modeling of signaling pathways and cell differentiation during development are in the fields of neural plasticity and brain development leading to quantum-weave dynamic patterns and specific molecular processes underlying extensive memory, learning, anticipation mechanisms and the emergence of human consciousness during the early brain development in children. Cell interactomics is here represented for the first time as a mixture of ‘classical’ states that determine molecular dynamics subject to Boltzmann statistics and ‘steady-state’, metabolic (multi-stable) manifolds, together with ‘configuration’ spaces of metastable quantum states emerging from complex quantum dynamics of interacting networks of biomolecules, such as proteins and nucleic acids that are now collectively defined as quantum interactomics. On the other hand, the time dependent evolution over several generations of cancer cells --that are generally known to undergo frequent and extensive genetic mutations and, indeed, suffer genomic transformations at the chromosome level (such as extensive chromosomal aberrations found in many colon cancers)-- cannot be correctly represented in the ‘standard’ terms of quantum automaton modules, as the normal somatic cells can. This significant difference at the cancer cell genomic level is therefore reflected in major changes in cancer cell interactomics often from one cancer cell ‘cycle’ to the next, and thus it requires substantial changes in the modeling strategies, mathematical tools and experimental designs aimed at understanding cancer mechanisms. Novel solutions to this important problem in carcinogenesis are proposed and experimental validation procedures are suggested. From a medical research and clinical standpoint, this approach has important consequences for addressing and preventing the development of cancer resistance to medical therapy in ongoing clinical trials involving stage III cancer patients, as well as improving the designs of future clinical trials for cancer treatments.\ud
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KEYWORDS: Emergence of Life and Human Consciousness;\ud
Proteomics; Artificial Intelligence; Complex Systems Dynamics; Quantum Automata models and Quantum Interactomics; quantum-weave dynamic patterns underlying human consciousness; specific molecular processes underlying extensive memory, learning, anticipation mechanisms and human consciousness; emergence of human consciousness during the early brain development in children; Cancer cell ‘cycling’; interacting networks of proteins and nucleic acids; genetic mutations and chromosomal aberrations in cancers, such as colon cancer; development of cancer resistance to therapy; ongoing clinical trials involving stage III cancer patients’ possible improvements of the designs for future clinical trials and cancer treatments. \ud
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M\"obius inversion formula for monoids with zero
The M\"obius inversion formula, introduced during the 19th century in number
theory, was generalized to a wide class of monoids called locally finite such
as the free partially commutative, plactic and hypoplactic monoids for
instance. In this contribution are developed and used some topological and
algebraic notions for monoids with zero, similar to ordinary objects such as
the (total) algebra of a monoid, the augmentation ideal or the star operation
on proper series. The main concern is to extend the study of the M\"obius
function to some monoids with zero, i.e., with an absorbing element, in
particular the so-called Rees quotients of locally finite monoids. Some
relations between the M\"obius functions of a monoid and its Rees quotient are
also provided.Comment: 12 pages, r\'esum\'e \'etendu soumis \`a FPSAC 201
The Tutte-Grothendieck group of a convergent alphabetic rewriting system
The two operations, deletion and contraction of an edge, on multigraphs
directly lead to the Tutte polynomial which satisfies a universal problem. As
observed by Brylawski in terms of order relations, these operations may be
interpreted as a particular instance of a general theory which involves
universal invariants like the Tutte polynomial, and a universal group, called
the Tutte-Grothendieck group. In this contribution, Brylawski's theory is
extended in two ways: first of all, the order relation is replaced by a string
rewriting system, and secondly, commutativity by partial commutations (that
permits a kind of interpolation between non commutativity and full
commutativity). This allows us to clarify the relations between the semigroup
subject to rewriting and the Tutte-Grothendieck group: the later is actually
the Grothendieck group completion of the former, up to the free adjunction of a
unit (this was even not mention by Brylawski), and normal forms may be seen as
universal invariants. Moreover we prove that such universal constructions are
also possible in case of a non convergent rewriting system, outside the scope
of Brylawski's work.Comment: 17 page
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