1 / 26

Designing Asynchronous Arbiters using Petri Nets

Designing Asynchronous Arbiters using Petri Nets. Alex Yakovlev Newcastle University, UK. What is an Arbiter?. Client 1. Client 2. Client 1. G. G. G. D. D. D. Adaptor 1. Adaptor 1. Adaptor 1. Example: “lazy token” ring adaptor. R. R. R. Client 1. Client 2. Client 1. G. G.

pink
Download Presentation

Designing Asynchronous Arbiters using Petri Nets

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Designing Asynchronous Arbiters using Petri Nets Alex Yakovlev Newcastle University, UK Dagstuhl Seminar

  2. What is an Arbiter? Dagstuhl Seminar

  3. Client 1 Client 2 Client 1 G G G D D D Adaptor 1 Adaptor 1 Adaptor 1 Example: “lazy token” ring adaptor R R R Dagstuhl Seminar

  4. Client 1 Client 2 Client 1 G G D D Adaptor 1 Example: “lazy token” ring adaptor R R R G D Lr Rr La Ra Adaptor 1 Adaptor 1 Dagstuhl Seminar

  5. R G D Rr Lr Ring adaptor Ra La Lazy ring adaptor Lr R dum dum G Rr La D Ra t=0 (token isn’t initially here) t=1 t=0 Dagstuhl Seminar

  6. Lazy ring adaptor Lr R R dum G D dum Rr Lr G Rr Ring adaptor Ra La La D Ra t=0->1->0 (token must be taken from the right and past to the left t=1 t=0 Dagstuhl Seminar

  7. Lazy ring adaptor Lr R R dum G D dum Rr Lr G Rr Ring adaptor Ra La La D Ra t=1 (token is already here) t=1 t=0 Dagstuhl Seminar

  8. Lazy ring adaptor Lr R R dum G D dum Rr Lr G Rr Ring adaptor Ra La La D Ra t=0->1 (token must be taken from the right) t=1 t=0 Dagstuhl Seminar

  9. Lazy ring adaptor Lr R R dum G D dum Rr Lr G Rr Ring adaptor Ra La La D Ra t=1 (token is here) t=1 t=0 Dagstuhl Seminar

  10. R G D Rr Lr Ring adaptor Ra La Lazy ring adaptor Lr R dum dum G Rr La D Ra t=0 (token isn’t initially here) t=1 t=0 Dagstuhl Seminar

  11. Arbitration refinement • Asynchronous circuits often require elements to resolveconflictswhich are intentionally “pre-programmed” in specifications • These elements are similar to semaphores (etc.) in concurrent programs • These elements are different from logical gates because they involve internally analogue components • The LPN model must be refined to explicitly “factorise” non-persistent behavior from the rest of the model – the latter can be synthesized using logic gates E.g. Request-Grant-Done (RGD) arbiter D RGD arbiter G1 R1 G2 R2 Dagstuhl Seminar

  12. Arbitration refinement E.g. Request-Grant-Done (RGD) arbiter p D RGD arbiter G1 R1 b a G2 R2 Dagstuhl Seminar

  13. Arbitration refinement E.g. Request-Grant-Done (RGD) arbiter p D RGD arbiter G1 R1 b a G2 R2 Assume a and b are circuit actions that are in conflict (may disable each other) and need to be protected Dagstuhl Seminar

  14. Arbitration refinement E.g. Request-Grant-Done (RGD) arbiter p p D G1 D RGD arbiter R1 R1 R2 me b a G2 R2 G1 G2 a Assume a and b are circuit actions that are in conflict (may disable each other) and need to be protected b Dagstuhl Seminar

  15. Arbitration refinement E.g. Request-Grant-Done (RGD) arbiter p p D G1 D RGD arbiter R1 R1 R2 me b a G2 R2 G1 G2 a b a and b are protected now (they are no longer disabled) Dagstuhl Seminar

  16. Translation of LPNs to circuits • After appropriate refinements have been made one can translate Labelled Petri nets (or Signal Transition Graphs) into circuits • Either by syntax-direct translation • Or by using Logic Synthesis Dagstuhl Seminar

  17. Why direct translation? • Direct translation has linear complexity but can be area inefficient (inherent one-hot encoding) • Logic synthesis has problems with state space explosion, repetitive and regular structures (log-based encoding approach) Dagstuhl Seminar

  18. Direct Translation of Petri Nets • Previous work dates back to 70s • Synthesis into event-based(two-phase) circuits (similar to Sutherland’s micropipeline control) • S.Patil, F.Furtek (MIT) • Synthesis into level-based (4-phase) circuits (similar to synthesis from one-hot encoded FSMs) • R. David (’69, translation FSM graphs to CUSA cells) • L. Hollaar (’82, translation from parallel flowcharts) • V. Varshavsky et al. (’90,’96, translation from PN into an interconnection of David Cells) Dagstuhl Seminar

  19. Synthesis into event-based circuits • Patil’s translation method for simple PNs • Furtek’s extension to 1-safe net • “Pragmatic” extensions to Patil’s set (for non-simple PNs) • Examples: modulo-N counter, Lazy ring adapter Dagstuhl Seminar

  20. Patil’s set of modules Circuit equivalent: Petri net fragment: wire place inverter marked place C-element join C XOR merge fork fan-out Effectively RGD arbiter shared (conflict) place S switch Dagstuhl Seminar s

  21. Direct synthesis example(lazy token ring adapter) Exercise: Refine this initial LPN and map it (fragment-by-fragment) to the circuit Dagstuhl Seminar

  22. Synthesis by using Signal Transition Graphs • It is also possible to synthesise such Petri net specifications using automated async logic synthesis tools • Petrify is a tool which takes a Signal Transition Graph (STG) and returns a logic implementation • As an arbiter a two-way Mutual Exclusion element (MUTEX) is often used Dagstuhl Seminar

  23. Lr+ R+ me r2+ r1+ t=1 g1+ g2+ t=0 Rr+ Rr+ G+ s+ Ra+ Ra+ t- R r+ s+ La- G+ Rr- Rr+ La+ Lr- r1- R- Ra- Ra- Lr+ r2- r1- r2- g1- g2- G- s- La- Refined STG Dagstuhl Seminar

  24. G R r1 g1 ME r2 g2 Rr Lr La Ra Logic Circuit synthesised automatically with a tool Dagstuhl Seminar

  25. Points for further exploration • Sometimes it is hard to insert mutex events and then “factorise out” a simple 2-way mutex or RGD arbiter from the rest of the logic • For example, problematic cases are usually arbitration with multiple clients and multiple resources • A lot of manual effort is needed in decomposing an original model there Dagstuhl Seminar

  26. Example: 2-client 2-resource arbiter Difficult part is here Dagstuhl Seminar

More Related