Hybrid adaptive Petri nets: a conceptual framework for partial fluidization of Petri nets

Petri nets (PNs) constitute a well known family of formalisms for the modeling and analysis ofDiscrete Event Dynamic Systems (DEDS). As most formalisms for discrete event systems, PNssuffer from the state explosion problem, which renders enumerative analysis techniquesunfeasible for large systems. A technique to overcome the problem is to relax integralitycontraints of the discrete PN model, leading to continuous PN. This relaxation highly reducesthe complexity of analysis techniques but may not preserve important properties of theoriginal PN system such as deadlock‐freeness, liveness, reversibility, etc. This work focuses onHybrid Adaptive Petri nets (HAPNs), a Petri net based formalism in which the firing oftransitions is partially relaxed. The transitions of a HAPN can behave in two different modes:continuous mode for high transition workload, and discrete in other case. This way, a HAPN isable to adapt its behaviour to the net workload, it offers the possibility to represent morefaithfully the discrete model and use efficient analysis techniques by behaving as continuouswhen the load is high. Reachability space and the deadlock‐freeness property of hybridadaptive nets is studied in this work

Balancing Static Islands in Dynamically Scheduled Circuits using Continuous Petri Nets

High-level synthesis (HLS) tools automatically transform a high-level program, for example in C/C++, into a low-level hardware description. A key challenge in HLS is scheduling, i.e. determining the start time of all the operations in the untimed program. A major shortcoming of existing approaches to scheduling – whether they are static (start times determined at compile-time), dynamic (start times determined at run-time), or a hybrid of both – is that the static analysis cannot efficiently explore the run-time hardware behaviours. Existing approaches either assume the timing behaviour in extreme cases, which can cause sub-optimal performance or larger area, or use simulation-based approaches, which take a long time to explore enough program traces. In this article, we propose an efficient approach using probabilistic analysis for HLS tools to efficiently explore the timing behaviour of scheduled hardware. We capture the performance of the hardware using Timed Continous Petri nets with immediate transitions, allowing us to leverage efficient Petri net analysis tools for making HLS decisions. We demonstrate the utility of our approach by using it to automatically estimate the hardware throughput for balancing the throughput for statically scheduled components (also known as static islands) computing in a dynamically scheduled circuit. Over a set of benchmarks, we show that our approach on average incurs a 2% overhead in area-delay product compared to optimal designs by exhaustive search

Balancing static islands in dynamically scheduled circuits using continuous petri nets

High-level synthesis (HLS) tools automatically transform a high-level program, for example in C/C++, into a low-level hardware description. A key challenge in HLS is scheduling, i.e. determining the start time of all the operations in the untimed program. A major shortcoming of existing approaches to scheduling – whether they are static (start times determined at compile-time), dynamic (start times determined at run-time), or a hybrid of both – is that the static analysis cannot efficiently explore the run-time hardware behaviours. Existing approaches either assume the timing behaviour in extreme cases, which can cause sub-optimal performance or larger area, or use simulation-based approaches, which take a long time to explore enough program traces. In this article, we propose an efficient approach using probabilistic analysis for HLS tools to efficiently explore the timing behaviour of scheduled hardware. We capture the performance of the hardware using Timed Continous Petri nets with immediate transitions, allowing us to leverage efficient Petri net analysis tools for making HLS decisions. We demonstrate the utility of our approach by using it to automatically estimate the hardware throughput for balancing the throughput for statically scheduled components (also known as static islands) computing in a dynamically scheduled circuit. Over a set of benchmarks, we show that our approach on average incurs a 2% overhead in area-delay product compared to optimal designs by exhaustive search

Fluid approximation of Petri net models with relatively small populations

Fluidization is an appealing relaxation technique based on the removal of integrality constraints in order to ease the analysis of discrete Petri nets. The result of fluidifying discrete Petri nets are the so called Fluid or Continuous Petri nets. As with any relaxation technique, discrepancies among the behaviours of the discrete and the relaxed model may appear. Moreover, such discrepancies may have a comparatively bigger effect when the population of the system, the marking in Petri net terms, is “relatively” small. This paper proposes two complementary approaches to obtain a better fluid approximation of discrete Petri nets. The first one focuses on untimed systems and is based on the addition of places that are implicit in the untimed discrete system but not in the continuous. The idea is to cut undesired spurious solutions whose existence worsens the fluidization. The second one focuses on a particular situation that can severely affect the quality of fluidization in timed systems. Namely, such a situation arises when the enabling degree of a transition is equal to 1. This last approach aims to alleviate such a state of affairs, which is termed the bound reaching problem, on systems under infinite servers semantics

Estudio de nuevos extractos naturales para su incorporación en biopolímeros para el futuro desarrollo de films activos

El envasado activo consiste en la incorporación de agentes activos en el material de envase para obtener alimentos más seguros, de mayor calidad y con mayor vida útil. Esto se consigue con la incorporación de compuestos (agentes activos) de origen sintético o natural como extractos vegetales, aceites esenciales, etc; con capacidades antimicrobianas, antioxidantes, de absorción o emisión. Estos agentes son preferiblemente incorporados en polímeros biodegrables en vez de plásticos debido a la extensa polución provocada por su uso. En este trabajo hemos estudiado las propiedades antioxidantes y antimicrobianas de los aceites esenciales y extractos naturales, para incorporarlos en biopolímeros celulósicos y así crear films activos. Para ello usamos aceites de tomillo rojo y mostaza y extractos de equinacea purpúrea, equinacea angustifolia y alfalfa, que fueron sometidos a estudios de determinación de actividad antioxidante, como el 2,2-difenil-1-picrilhidracilo (DPPH) y la captación de radicales libres, así como la evaluación de su susceptibilidad antimicrobiana mediante la determinación de la Concentración Mínima Inhibitoria (MIC) y la Concentración Mínima Bactericida (MBC). Después, los más activos se incorporaron en los biopolímeros celulósicos. Nuestros resultados mostraron que el aceite esencial de tomillo era el mejor para realizar films activos, debido a tener una IC50 de 16 mg/g y valores de MIC y MBC inferiores a 1 mg/mL (0,25 mg/mL y 0,5 mg/mL para ambas MIC y MCB en E.coli and L. monocytogenes respectivamente); sin embargo, su miscibilidad con la carboximetil celulosa era problemática y peor que la de equinacea purpúrea; esto llevó a su incorporación en complejos de inclusión con ciclodextrina para mejorar la miscibilidad. La carboximetilcelulosa de sodio se secaba mejor, estando menos pegada a la placa. Concluimos que el film de carboximetilcelulosa de sodio con aceite esencial de tomillo rojo tiene las mejores propiedades, teniendo potencial para ser un buen material para el envasado activo. <br /

A Hybrid Learning Space for Physically-Active Mathematics: the case of Numberfit

This paper presents the case study of an intervention called Numberfit that aims at capturing primarily students’ interest in mathematics by combining team games and physical activity. We describe the hybrid learning space that is created through this approach that includes an online platform that allows the teachers and facilitators to design a lesson plan, input student scores and visualise a leaderboard. At the same time, various digital and tangible resources engage students in group (collaborative or competitive) activities while practising a range of topics in mathematics. We examine the changing role of the teacher and provide some methodological insights for conducting research in relation to student’s affect, motivation and behaviour in this context

Integer Vector Addition Systems with States

This paper studies reachability, coverability and inclusion problems for Integer Vector Addition Systems with States (ZVASS) and extensions and restrictions thereof. A ZVASS comprises a finite-state controller with a finite number of counters ranging over the integers. Although it is folklore that reachability in ZVASS is NP-complete, it turns out that despite their naturalness, from a complexity point of view this class has received little attention in the literature. We fill this gap by providing an in-depth analysis of the computational complexity of the aforementioned decision problems. Most interestingly, it turns out that while the addition of reset operations to ordinary VASS leads to undecidability and Ackermann-hardness of reachability and coverability, respectively, they can be added to ZVASS while retaining NP-completness of both coverability and reachability.Comment: 17 pages, 2 figure

Approaching the Coverability Problem Continuously

The coverability problem for Petri nets plays a central role in the verification of concurrent shared-memory programs. However, its high EXPSPACE-complete complexity poses a challenge when encountered in real-world instances. In this paper, we develop a new approach to this problem which is primarily based on applying forward coverability in continuous Petri nets as a pruning criterion inside a backward coverability framework. A cornerstone of our approach is the efficient encoding of a recently developed polynomial-time algorithm for reachability in continuous Petri nets into SMT. We demonstrate the effectiveness of our approach on standard benchmarks from the literature, which shows that our approach decides significantly more instances than any existing tool and is in addition often much faster, in particular on large instances.Comment: 18 pages, 4 figure

Loop Summarization with Rational Vector Addition Systems

This paper presents a technique for computing numerical loop summaries. The method synthesizes a rational vector addition system with resets ( ℚ -VASR) that simulates the action of an input loop, and then uses the reachability relation of that ℚ -VASR to over-approximate the behavior of the loop. The key technical problem solved in this paper is to automatically synthesize a ℚ -VASR that is a best abstraction of a given loop in the sense that (1) it simulates the loop and (2) it is simulated by any other ℚ -VASR that simulates the loop. Since our loop summarization scheme is based on computing the exact reachability relation of a best abstraction of a loop, we can make theoretical guarantees about its behavior. Moreover, we show experimentally that the technique is precise and performant in practice