scholarly journals Characterizations of consistent marked graphs

2003 ◽  
Vol 127 (2) ◽  
pp. 357-371 ◽  
Author(s):  
Fred S Roberts ◽  
Shaoji Xu
Keyword(s):  
2017 ◽  
Vol 26 (12) ◽  
pp. 1750081
Author(s):  
Sang Youl Lee

In this paper, we introduce a notion of virtual marked graphs and their equivalence and then define polynomial invariants for virtual marked graphs using invariants for virtual links. We also formulate a way how to define the ideal coset invariants for virtual surface-links using the polynomial invariants for virtual marked graphs. Examining this theory with the Kauffman bracket polynomial, we establish a natural extension of the Kauffman bracket polynomial to virtual marked graphs and found the ideal coset invariant for virtual surface-links using the extended Kauffman bracket polynomial.


2014 ◽  
pp. 55-66 ◽  
Author(s):  
King Sing Cheung
Keyword(s):  

2014 ◽  
pp. 33-53
Author(s):  
King Sing Cheung
Keyword(s):  

2022 ◽  
Vol 15 (1) ◽  
pp. 1-32
Author(s):  
Lana Josipović ◽  
Shabnam Sheikhha ◽  
Andrea Guerrieri ◽  
Paolo Ienne ◽  
Jordi Cortadella

Commercial high-level synthesis tools typically produce statically scheduled circuits. Yet, effective C-to-circuit conversion of arbitrary software applications calls for dataflow circuits, as they can handle efficiently variable latencies (e.g., caches), unpredictable memory dependencies, and irregular control flow. Dataflow circuits exhibit an unconventional property: registers (usually referred to as “buffers”) can be placed anywhere in the circuit without changing its semantics, in strong contrast to what happens in traditional datapaths. Yet, although functionally irrelevant, this placement has a significant impact on the circuit’s timing and throughput. In this work, we show how to strategically place buffers into a dataflow circuit to optimize its performance. Our approach extracts a set of choice-free critical loops from arbitrary dataflow circuits and relies on the theory of marked graphs to optimize the buffer placement and sizing. Our performance optimization model supports important high-level synthesis features such as pipelined computational units, units with variable latency and throughput, and if-conversion. We demonstrate the performance benefits of our approach on a set of dataflow circuits obtained from imperative code.


1992 ◽  
Vol 15 (3) ◽  
pp. 282-295 ◽  
Author(s):  
Hauke Jungnitz ◽  
Beatriz Sánchez ◽  
Manuel Silva
Keyword(s):  

1991 ◽  
Vol 5 (2) ◽  
pp. 145-157 ◽  
Author(s):  
F. Baccelli ◽  
N. Bambos ◽  
J. Walrand

In this work, the discrete event systems called Stochastic Marked Graphs (SMGs) are investigated from a stability point of view. Being a special class of Timed Petri Nets with stochastic firing times, they are studied under general assumptions of stationarity and ergodicity of the firing times and ergodicity of flows of their free strongly connected components. The values of the flows of tokens in an SMG are specified as functions of the intrinsic rates of its free strongly connected components, and various stability issues are discussed.


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