Negative Tokens Research Articles

Structural matrices for Signed Petri net

The developments in the field of Graph Theory and Petri net Theory in the form of balanceness and negative tokens respectively motivated the authors to bridge the gap between Petri net and Signed graph and introduce a new concept of Signed Petri net (SPN). In Petri net theory, matrices have been used to describe the structural behavior of the Petri net. Such matrices have been introduced for SPN which help in identifying relationships among the transitions and places of an SPN. Various subclasses of SPN are given along with characterizations of these subclasses using the matrices introduced. We consider ordinary SPNs (i.e. SPNs without multiple arcs) in the paper.

Marking the unexpected: The case of ba in Greek talk-in-interaction

This article examines the Greek particle ba in naturally occurring talk, adopting a conversation analytic perspective. The analysis reveals that it is systematically involved in two different types of social action, depending on prosodic variation and sequential position. Overall, ba appears as either a repair initiator expressing surprise, or a negative token in polar answers and disagreements. It is shown that these seemingly different uses are united by an indexical anchor of unexpectedness that is realized differently prosodically and adopts an either backward- or forward-looking orientation. The article gives further insight into how one's knowledge is related to one's expectations, thus contributing to a better understanding of the epistemics of (un)expectedness. It also enriches growing cross-linguistic literature on epistemic particles from a Greek perspective. Data are drawn from 40 recorded ordinary conversations included in the Corpus of Spoken Greek and 8 focus groups conducted in Greece.

Executions in (Semi-)Integer Petri Nets are Compact Closed Categories

In this work, we analyse Petri nets where places are allowed to have a negative number of tokens. For each net we build its correspondent category of executions, which is compact closed, and prove that this procedure is functorial. We moreover exhibit a procedure to recover the original net from its category of executions, show that it is again functorial, and that this gives rise to an adjoint pair. Finally, we use compact closeness to infer that allowing negative tokens in a Petri net makes the causal relations between transition firings non-trivial, and we use this to model interesting phenomena in economics and computer science.

The Use of Response Tokens In Waiting for Godot by Samuel Beckett

This study discusses the use of response tokens in Waiting for Godot written by Samuel Beckett. Specifically, it examines kinds and the functions of response tokens uttered by the main characters. This research uses descriptive approach to obtain rich description and to understand response tokens in Waiting for Godot. The data were taken form Vladimir's and Estragon's utterances. The key findings suggest that the types of response tokens in the drama are single response token, response token preceding expanded response, premodified response token, negative token and doublet and also triplet token. Meanwhile, the functions of response token include the function of continuers, acknowledgement, newsmarker, change-of-activity, assessement and brief question token.

Steady state analysis of timed event graphs with time window constraints

For discrete event systems, time window constraints between two events are often required to control their behavior. Such time constrained discrete event systems are found in various industrial systems such as chemical vapor deposition processes for wafer fabrication, electroplating lines for printed circuit board fabrication, microcircuit design etc. A negative event graph (NEG) which is an extension of the timed event graph (TEG) has been proposed by Lee and Park (2005) to model and analyze discrete event systems with time window constraints. An NEG can model time window constraints between any two transitions by introducing negative places and negative tokens. This study examines the steady state behavior of an NEG that satisfies the time window constraints. We develop a recurrent equation for the feasible steady firing epochs based on the minimax algebra. In addition, we identify four classes of steady states that correspond to the earliest and latest feasible steady firing schedules for each of the minimum and maximum cycle times by extending the steady state results of a conventional TEG based on the minimax algebra. Besides, we characterize how the cycle times and the steady schedules are computed through the matrix algebra and the associated graph algorithms.

An Extended Event Graph With Negative Places and Tokens for Time Window Constraints

We introduce places with negative holding times and tokens with negative token counts into a timed event graph in order to model and analyze time window constraints. We extend the enabling and firing rules for such an extended event graph named a negative event graph (NEG). We develop necessary and sufficient conditions based on the circuits for which the NEG is live, that is, an infinite sequence of feasible firing epochs exist for each transition. We prove that the minimum cycle time is the same as the maximum circuit ratio of the circuits with positive token counts. We also show that when there exists circuits with negative token counts, the maximum cycle time is bounded and the same as the minimum circuit ratio of such circuits. A scheduling example for a robot-based cluster tool with wafer residency time constraints for semiconductor manufacturing is explained. Note to Practitioners-Scheduling and control problems for modern man-made systems, including automated manufacturing systems such as cluster tools for semiconductor manufacturing, microcircuits, and real-time software systems, are usually modeled as discrete event systems. Such systems often have strict time constraints on timings of some events. Our results can be used for identifying whether there can be a feasible schedule that satisfies all time constraints, computing the range of the feasible cycle times, and determining a steady schedule with the minimum cycle time. By using the feasibility condition, we also can accommodate the system configuration, the task times, and the task sequence so that the system can satisfy the time constraints while meeting the target cycle time. Such practice is already used for real cluster tool engineering. We have more results on implementing a real-time scheduler and controller for time constrained systems.