Race Free Assignment Of Rights


Once a reduced flow table has been derived for an asynchronous sequential circuit, the next step in the design is to assign binary variables to each stable state. This assignment results in the transformation of the flow table into its equivalent transition table. The primary objective in choosing a proper binary state assignment is the prevention of critical races. Critical races can be avoided by making a binary state assignment in such a way that only one variable changes at any given time when a state transition occurs in the flow table.

ü Three-Row Flow-Table Example

Fig: Three row flow table example

To avoid critical races, we must find a binary state assignment such that only one binary variable changes during each state transition. An attempt to find such an assignment is shown in the transition diagram. State a is assigned binary 00, and state c is assigned binary 11. This assignment will ca use a critical race during the transition from a to c because there are two changes in the binary state variables and the transition from a to c may occur directly or pass through b. Note that the transition from c to a also ca uses a race condition, but it is noncritical because the transition does not pass through other states.

A race-free assignment can be obtained if we add an extra row to the flow table. The use of a fourth row does not increase the number of binary state variables, but it allows the formation of cycles between two stable states.

The transition table corresponding to the flow table with the indicated binary state assignment is shown in Fig. The two dashes in row d represent unspecified states that can be considered don't-care conditions. However, care must be taken not to assign 10 to these squares, in order to avoid the possibility of an unwanted stable state being established in the fourth row.

ü    Four-Row Flow-Table Example

A flow table with four rows requires a minimum of two state variables. Although a race-free assignment is sometimes possible with only two binary state variables, in many cases the requirement of extra rows to avoid critical races will dictate the use of three binary state variables

Fig: Four-row flow-table example

The following figure shows a state assignment map that is suitable for any four-row flow table. States a, b, c and d are the original states and e, f and g are extra states. The transition from a to d must be directed through the extra state e to produce a cycle so that only one binary variable changes at a time. Similarly, the transition from c to a is directed through g and the transition from d to c goes through f. By using the assignment given by the map, the four-row table can be expanded to a seven-row table that is free of critical races.

Fig: Choosing extra rows for the flow table

Note that although the flow table has seven rows there are only four stable states. The uncircled states in the three extra rows are there merely to provide a race-free transition between the stable states.

Fig: State assignment to modified flow table

ü    Multiple-Row Method

The method for making race-free stale assignments by adding extra rows in the flow table is referred to as the shared-row method. A second method called the multiple-row method is not as efficient, but is easier to apply. In multiple- row assignment each state in the original row table is replaced by two or more combinations of state variables.

Fig: Multiple row assignment

There are two binary state variables for each stable state, each variable being the logical complement of the other. For example, the original state a is replaced with two equivalent states a1 =000 and a2 = 111. The output values, not shown here must be the same in a1 and a2. Note that a1 is adjacent to b1, c2 and d1, and a2 is adjacent to c1, b2 and d2, and similarly each state is adjacent to three states with different letter designations.

The expanded table is formed by replacing each row of the original table with two rows. In the multiple-row assignment, the change from one stable state 10 another will always cause a change of only one binary state variable. Each stable stale has two binary assignments with exactly the same output.

A responsibility assignment matrix[1] (RAM), also known as RACI matrix[2] or linear responsibility chart[3] (LRC), describes the participation by various roles in completing tasks or deliverables for a project or business process.[4] It is especially useful in clarifying roles and responsibilities in cross-functional/departmental projects and processes.[5]

RACI is an acronym derived from the four key responsibilities most typically used: Responsible, Accountable, Consulted, and Informed.[6]

Key responsibility roles (RACI model )[edit]

R=Responsible, A=Accountable, C=Consulted, I=Informed

Responsible (also Recommender)
Those who do the work to achieve the task.[7] There is at least one role with a participation type of responsible, although others can be delegated to assist in the work required (see also RASCI below for separately identifying those who participate in a supporting role).
Accountable (also Approver or final approving authority)
The one ultimately answerable for the correct and thorough completion of the deliverable or task, and the one who delegates the work to those responsible.[7] In other words, an accountable must sign off (approve) work that responsible provides. There must be only one accountable specified for each task or deliverable.[4]
Consulted (sometimes Consultant or counsel)
Those whose opinions are sought, typically subject matter experts; and with whom there is two-way communication.[7]
Informed (also Informee)
Those who are kept up-to-date on progress, often only on completion of the task or deliverable; and with whom there is just one-way communication.[7]

Very often the role that is accountable for a task or deliverable may also be responsible for completing it (indicated on the matrix by the task or deliverable having a role accountable for it, but no role responsible for its completion, i.e. it is implied). Outside of this exception, it is generally recommended that each role in the project or process for each task receive, at most, just one of the participation types. Where more than one participation type is shown, this generally implies that participation has not yet been fully resolved, which can impede the value of this technique in clarifying the participation of each role on each task.

Role distinction[edit]

There is a distinction between a role and individually identified people: a role is a descriptor of an associated set of tasks; may be performed by many people; and one person can perform many roles. For example, an organization may have ten people who can perform the role of project manager, although traditionally each project only has one project manager at any one time; and a person who is able to perform the role of project manager may also be able to perform the role of business analyst and tester.

Assigning people to facilities[edit]

The matrix is typically created with a vertical axis (left-hand column) of tasks (from a work breakdown structure) or deliverables (from a product breakdown structure), and a horizontal axis (top row) of roles (from an organizational chart).

CodeNameProject sponsorBusiness analystProject managerTechnical architectApplications development
Stage AManage sales
Stage BAssess job
Stage CInitiate project
- C04Security governance (draft)CCAII
- C10Functional requirementsARICI
- C11Business acceptance criteriaARICI
Stage DDesign solution

Another example from the maintenance and reliability community


There are a number of alternatives to the RACI participation types:


This is an early version[8] of a Responsibility Assignment Matrix, with the roles defined as:
Review Required
Input Required
Sign-off Required


This is a version very useful to organizations where the output of activities under the accountability of a single person/function can be reviewed and vetoed by multiple stakeholders, due to the collaborative nature of the culture.
The person/function carrying out the activity.
The person/function ultimately answerable for the correct and thorough completion of the deliverable or task, and often the one who delegates the work to the performer.
The person/function reviewing the result of the activity (other than the accountable). He or she has a right of veto; his or her advice is binding.
The person/function consulted to give advice based upon recognized expertise. The advice is non-binding.
The person/function who must be informed of the result of the activity.


This is an expanded version[9] of the standard RACI, less frequently known as RASCI,[10] breaking the responsible participation into:
Those responsible for the task, who ensure that it is done as per the approver
Resources allocated to responsible. Unlike consulted, who may provide input to the task, support helps complete the task.


This is an alternative version[11][12] of the standard RACI, foregoing the consulted participation and replacing it with:
Resources which play a supporting role in implementation.


This is an expanded version of the standard RACI, with an additional participation type:
Quality Review
Those who check whether the product meets the quality requirements.


This is an expanded version[6] of the standard RACI, with two additional participation types:
Those who check whether the product meets the acceptance criteria set forth in the product description.
Those who approve the verify decision and authorize the product hand-off. It seems to make sense that the signatory should be the party being accountable for its success.


This is an expanded version,[13] of the standard RACI, also known as RACIO[14] with one additional participation type.
Out of the loop (or omitted)
Designating individuals or groups who are specifically not part of the task. Specifying that a resource does not participate can be as beneficial to a task's completion as specifying those who do participate.


Another version that has been used to centralize decision making, and clarify who can re-open discussions.[15]
A single driver of overall project like the person steering a car.
One or more approvers who make most project decisions, and are responsible if it fails.
Are the worker-bees who are responsible for deliverables; and with whom there is two-way communication.
Those who are impacted by the project and are provided status and informed of decisions; and with whom there is one-way communication.


Another tool used to clarify decision roles and thereby improve decision making overall is RAPID®, which was created by and is a registered trademark of Bain & Company.
The Recommend role typically involves 80 percent of the work in a decision. The recommender gathers relevant input and proposes a course of action—sometimes alternative courses, complete with pros and cons so that the decision maker's choices are as clear, simple and timely as possible.
The Agree role represents a formal approval of a recommendation. The 'A' and the 'R' should work together to come to a mutually satisfactory proposal to bring forward to the Decider. But not all decisions will need an Agree role, as this is typically reserved for those situations where some form of regulatory or compliance sign-off is required.
The Perform role defines who is accountable for executing or implementing the decision once it is made. Best-practice companies typically define P's and gather input from them early in the process
The Input role provides relevant information and facts so that the Recommender and Decider can assess all the relevant facts to make the right decision. However, the 'I' role is strictly advisory. Recommenders should consider all input, but they don't have to reflect every point of view in the final recommendation.
The Decide role is for the single person who ultimately is accountable for making the final decision, committing the group to action and ensuring the decision gets implemented.


Another tool used in organisation design or roles analysis.
Identify who is in charge of making sure the work is done.
Identify who has final decision power on the work.
Identify who actually does the work.
Identify who is involved to provide support to the work.
Identify who is informed that the work has been done (or will be started)


A variant of RASCI developed by three Whitehall theorists (Kane, Jackson, Gilbert). This scheme is adapted for use in matrix management environments, and differs only from RASCI in having an additional role of Driver and a narrower definition of Support:
An individual or party that assists those who are Responsible for delivering a task by both producing supporting collateral and setting timescales for delivery in line with the overarching aim of the individual or party who is Accountable for the overall accomplishment of the objective. The distinction between Driver and Support lies in that the former reinforces and clarifies the parameters of the task on behalf of those who are Accountable, while the latter refers to those who help those who are Responsible in reaching a given goal.


There are also a number of variations to the meaning of RACI participation types:

RACI (alternative scheme)[edit]

There is an alternative coding, less widely published but used by some practitioners and process mapping software, which modifies the application of the R and A codes of the original scheme. The overall methodology remains the same but this alternative avoids potential confusion of the terms accountable and responsible, which may be understood by management professionals but not always so clearly differentiated by others:
Those responsible for the performance of the task. There should be exactly one person with this assignment for each task.
Those who assist completion of the task
Those whose opinions are sought; and with whom there is two-way communication.
Those who are kept up-to-date on progress; and with whom there is one-way communication.

ARCI (decisions)[edit]

This alternative is focused only on documenting who has the authority to make which decisions. This can work across all sized work groups.
Authorized to approve an answer to the decision.
Responsible to recommend an answer to the decision.
Those whose opinions are sought; and with whom there is two-way communication.
Those who are informed after the decision is made; and with whom there is one-way communication.


External links[edit]

RACIQ Chart from project management simulator SimulTrain.
  1. ^" Organization Charts and Position Descriptions". A Guide to the Project Management Body of Knowledge (PMBOK Guide) (5th ed.). Project Management Institute. 2013. p. 262. ISBN 978-1-935589-67-9. 
  2. ^Jacka, Mike; Keller, Paulette (2009). Business Process Mapping: Improving Customer Satisfaction. John Wiley and Sons. p. 257. ISBN 0-470-44458-4. 
  3. ^Cleland, David; Ireland, Lewis (2006). Project management: strategic design and implementation. McGraw-Hill Professional. p. 234. ISBN 0-07-147160-X. 
  4. ^ abMargaria, Tiziana (2010). Leveraging Applications of Formal Methods, Verification, and Validation: 4th International Symposium on Leveraging Applications, Isola 2010, Heraklion, Crete, Greece, October 18–21, 2010, Proceedings, Part 1. Springer. p. 492. ISBN 3-642-16557-5. 
  5. ^Brennan, Kevin (2009). A Guide to the Business Analysis Body of Knowledge (BABOK Guide). International Institute of Business Analysis. p. 29. ISBN 0-9811292-1-8. 
  6. ^ abBlokdijk, Gerard (2008). The Service Level Agreement SLA Guide - SLA Book, Templates for Service Level Management and Service Level Agreement Forms. Fast and Easy Way to Write Your SLA. Lulu. p. 81. ISBN 1-921523-62-X. 
  7. ^ abcdSmith, Michael (2005). Role & Responsibility Charting (RACI)(PDF). Project Management Forum. p. 5. 
  8. ^A Guide to the Project Management Body of Knowledge. Project Management Institute. 2000. p. 111. ISBN 1-880410-22-2. 
  9. ^Hightower, Rose (2008). Internal controls policies and procedures. John Wiley & Sons. p. 83. ISBN 0-470-28717-9. 
  10. ^Baker, Dean (2009). Multi-Company Project Management: Maximizing Business Results Through Strategic Collaboration. J Ross. p. 58. ISBN 1-60427-035-7. 
  11. ^Mikes, Joe; Denton, Tara (2011). Training Speeds Continuous Improvement. Life Cycle Engineering. 
  12. ^Glossary. MG Rush. 2014. Archived from the original on 2004-10-31. 
  13. ^Bolman, Lee (2008). Reframing organizations: artistry, choice, and leadership. John Wiley & Sons. p. 112. ISBN 0-7879-8799-9. 
  14. ^Dickstein, Dennis (2008). No Excuses: A Business Process Approach to Managing Operational Risk. John Wiley & Sons. ISBN 0-470-48110-2. 
  15. ^Kendrick, Tom (2006). Results without authority: controlling a project when the team doesn't report to you. AMACOM Books, division of the American Management Association. p. 106. ISBN 0-8144-7343-1. 
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