The Glory of the Past and Geometrical Concurrency

This paper contributes to the general understanding of the "geometrical model of concurrency" that was named higher dimensional automata (HDAs) by Pratt and van Glabbeek. In particular we provide some understanding of the modal logics for such models and their expressive power in terms of the bisimulation that can be captured.The geometric model of concurrency is interesting from two main reasons: its generality and expressiveness, and the natural way in which autoconcurrency and action refinement are captured.Logics for this model, though, are not well investigated, where a simple, yet adequate, modal logic over HDAs was only recently introduced.As this modal logic, with two existential modalities, "during" and "after", captures only split bisimulation, which is rather low in the spectrum of van Glabbeek and Vaandrager, the immediate question was what small extension of this logic could capture the more fine-grained hereditary history preserving bisimulation (hh)?In response, the work in this paper provides several insights. One is the fact that the geometrical aspect of HDAs makes it possible to use for capturing the hh-bisimulation, a standard modal logic that does not employ event variables, opposed to the two logics (over less expressive models) that we compare with. The logic that we investigate here uses standard backward-looking modalities (i.e., past modalities) and extends the previously introduced logic (called HDML) that had only forward, action-labelled, modalities.Since the direct proofs are rather intricate, we try to understand better the above issues by introducing a related model that we call ST-configuration structures, which extend the configuration structures of van Glabbeek and Plotkin. We relate this model to HDAs, and redefine and prove the earlier results in the light of this new model. These offer a different view on why the past modalities and geometrical concurrency capture the hereditary history preserving bisimulation.Additional correlating insights are also gained.

Yoga and The Physics of Higher States of Consciousness

Higher states of consciousness are developed by meditation, defined by Patanjali as that which transforms focused attention into pure consciousness, the 4th state of pure consciousness - a major state in its own right, with its own physics, that of ‘experience information'. Phenomenologies of states 5 to 7 are explained from the perspective of modern physics and quantum cosmology. The role of the 5th state in life is to make possible witnessing states 1 to 3 resulting in ‘Perfection in Action'. Refinement of perception involved in the 6th State results in hearing the Cosmic Om, seeing the Inner Light, and seventh sense perception. All require special amplification processes on pathways of perception. Unity and Brahman Consciousness and their development are discussed with examples from the great sayings of the Upanishads, and similar cognitions like those of poet, Thomas Traherne. Throughout, supporting physics is given, particularly that of experience information, and its implications for Schrodinger's cat paradox and our scientific understanding of the universe as a whole.

Fuzzy Labeled Transition Refinement Tree

This paper aims to provide a formal framework that supports an incremental development of dynamic systems such as multi agents systems (MAS). We propose a fuzzy labeled transition system model (FLTS for short). FLTS allows a concise action refinement representation and deals with incomplete information through its fuzziness representation. Afterward, based on FLTS model, we propose a refinement model called fuzzy labeled transition refinement tree (FLTRT for short). The FLTRT structure serves as a tree of potential concurrent design trajectories of the system. Also, we introduce bisimulation relations for both models in order to identify equivalent design trajectories, which could be assessed with respect to relevant design parameters.

Open Fuzzy Synchronized Petri Net

Designing Multi agent systems needs a high-level specification model which supports abstraction, dynamicity, openness and enables fuzziness. Since the model of Synchronized Petri Nets supports dynamicity and abstraction, we extend it by fuzziness, openness and interaction with environment. The proposed model called Open Fuzzy Synchronized Petri Nets (OFSyPN for short) associates action name with transitions and enables openness feature and interaction with environment. Each action has an uncertainty degree and places are typed. The authors give an operational semantics for OFSyPN in terms of Fuzzy Labeled Transition System (FLTS for short). FLTS is a semantics model, which allows a concise action refinement representation and deals with incomplete information through its fuzziness representation. Furthermore the structure can be used to produce a tree of potential concurrent design trajectories, named fuzzy labeled transition refinement tree (FLTRT for short). We exemplify the OFSyPN model thought a case study.

Fuzzy Labeled Transition Refinement Tree

This paper aims to provide a formal framework that supports an incremental development of dynamic systems such as multi agents systems (MAS). We propose a fuzzy labeled transition system model (FLTS for short). FLTS allows a concise action refinement representation and deals with incomplete information through its fuzziness representation. Afterward, based on FLTS model, we propose a refinement model called fuzzy labeled transition refinement tree (FLTRT for short). The FLTRT structure serves as a tree of potential concurrent design trajectories of the system. Also, we introduce bisimulation relations for both models in order to identify equivalent design trajectories, which could be assessed with respect to relevant design parameters.

Validating Component-Based Implementations of Business Processes

This chapter provides a formal specification of non-atomic, relaxed action refinement suited for component-based business process engineering. Engineering a business process involves multiple process models created by different people on different levels of abstractions. Keeping the models consistent during the engineering procedure—refinement validation—is one objective of this chapter. In component-based software engineering, the lowest abstraction of a business process is mapped on existing components that have a description of their behaviors. Checking the consistency of process and component behavior—grounding validation—is the second objective. Both refinement and grounding validation increase the robustness of business process implementations and the productivity of process engineers. Technically, the specification given in this chapter is in terms of deadlock analysis in safe Petri nets. The evaluation of this straight-forward implementation underlines the exponential complexity of deadlock analysis in safe Petri nets. For use cases with more than 30 activities per process or heavy parallelism, optimized implementations are needed.