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Logical and concurrent thinking: decisions and dependencies

Write the condition that controls each decision, trace its effect on the next step and work out which tasks can overlap safely. Covers OCR A-Level H446 Paper 2 sections 2.1.4 and 2.1.5.

Content owner: Michael Print · Written for A-Level learners · Checked against official specifications

The short answer

Thinking logically identifies decision points, the Boolean conditions that govern them and the paths followed when those conditions are true or false. Thinking concurrently identifies tasks that can make progress during overlapping time periods and the dependencies that make other tasks wait.

Concurrency can overlap waiting or use multiple processing resources, but it also needs coordination. Parallelism means work actually executes at the same instant; concurrent tasks may instead take turns on one processor.

Before you start

Recognise if/else and true/false values. Review the selection and loops guide for basic control flow. The timing examples use invented durations, so no concurrency library is needed.

By the end, you should be able to

Translate a rule using AND, OR and NOT with suitable brackets.
Trace which branch executes, including boundary inputs.
Identify independent tasks and tasks that depend on earlier results.
Evaluate a concurrency benefit alongside overhead or shared-state risks.

Translate the whole rule before choosing a branch

A visitor needs a ticket and must either be aged at least 16 or be accompanied by an adult. Treat all three inputs as already validated.

Translate each condition into a Boolean input

T: Has a ticket
A: Aged at least 16
G: Accompanied by an adult

The admission condition is T AND (A OR G). The OR gives two ways to satisfy the age/supervision part; AND makes the ticket compulsory in both cases.

Admission rule: T AND (A OR G), where 1 means true
T	A	G	A OR G	Admit
0	0	0	0	0
0	0	1	1	0
0	1	0	1	0
0	1	1	1	0
1	0	0	0	0
1	0	1	1	1
1	1	0	1	1
1	1	1	1	1

An inclusive OR is true if either or both operands are true. It does not mean “exactly one”. The rejected condition is NOT T OR (NOT A AND NOT G): a missing ticket is enough to reject, or both age and supervision conditions fail.

Worked example

Follow the decision points in order

Instead of returning only true/false, the centre wants a message explaining rejection. The first decision checks the ticket; the second decision is reached only after the visitor passes that check.

Complete activity-centre admission examplePython

def admission(has_ticket, age, with_adult):
    if not has_ticket:
        return "No ticket"
    elif age >= 16 or with_adult:
        return "Admit"
    else:
        return "Adult required"

print(admission(True, 16, False))
print(admission(True, 15, False))
print(admission(False, 15, True))

Ticket, age 16, no adult: not has_ticket is false. The second condition is true because 16 >= 16; output Admit.
Ticket, age 15, no adult: the ticket check passes, but both parts of the second condition are false; output Adult required.
No ticket, age 15, adult present: the first condition is true; output No ticket. The return ends this call, so the age/supervision decision is never reached.

The outputs are those three messages on separate lines. Test age 15 and 16 together: changing >= to > would wrongly reject the boundary case.

Draw the dependencies before overlapping tasks

A publishing tool receives a completed document. A produces its thumbnail; B builds its text index; C packages both results. A and B read fixed input and write separate outputs. C must wait for both.

Overlap independent work, then join the results

Illustrative timings: adequate independent resources and no coordination overhead. The worked example below adds that overhead.

Task dependencies and invented execution times
Task	Duration	Must wait for
A: thumbnail	6 seconds	Document ready
B: text index	4 seconds	Document ready
C: assemble package	2 seconds	A and B complete

“Both tasks use the document” does not by itself create a dependency: two readers can use an unchanged document. If one task modifies it while the other reads, the safety of that overlap needs a different analysis.

Worked example

Calculate an overlap, then include its cost

Sequential execution: A, B and C take 6 + 4 + 2 = 12 seconds.
Ideal overlap: A and B start at time 0 on sufficient resources. B finishes at 4 seconds, but C still waits for A until time 6.
Join and finish: C runs from time 6 to time 8. The ideal total is max(6, 4) + 2 = 8 seconds.
Account for overhead: if starting and coordinating the tasks adds a further 1 second to this schedule, total time is 9 seconds. The saving over sequential execution is 3 seconds.

This model assumes both tasks retain their stated durations when they overlap. A saturated disk, network connection or single CPU can change that assumption. Short tasks may save less time than the coordination costs.

Evaluate what the tasks share

Concurrency can improve responsiveness: a user interface may accept input while another task waits for a download. Independent computation can also finish sooner using multiple processors. The tradeoffs include more memory, scheduling overhead, communication and more difficult testing because the order of events can vary.

A lost update when two tasks share an unsafe counter
Step	Task A	Task B	Shared count
1	Reads 10		10
2		Reads 10	10
3	Writes 10 + 1		11
4		Writes 10 + 1	11

Both tasks intended to add one, but the final count is 11 instead of 12. This race condition makes correctness depend on the timing of shared operations.

Protect the whole read–modify–write operation with appropriate synchronisation. Protecting only the final write does not prevent the lost update.

Useful design choices include separate outputs followed by a controlled merge, an atomic update, or a lock around shared changes. Coordination can make tasks wait, so include it when evaluating the benefit.

Try it yourself

These four original questions total 15 marks. Solutions give indicative guidance, not an OCR mark scheme.

Question 1

4 marks

A loan is permitted only if a member is active (M) and either has paid the deposit (P) or has a valid exemption (V). Write a Boolean condition. Give one set of input values showing why (M AND P) OR V would be incorrect, and state both results.

Show solution and marking guidance

Indicative answer

M AND (P OR V) (1 for requiring M, 1 for grouping the two alternatives).
With M = false, P = false, V = true, the intended condition is false (1), whereas (M AND P) OR V is true (1).
Accept an equivalent counterexample with M false and V true.

Question 2

3 marks

Using admission(), give the outputs of these calls in order: admission(False, 20, False), admission(True, 14, True), admission(True, 14, False).

Show solution and marking guidance

Indicative answer: No ticket (1); Admit (1); Adult required (1), in that order. The first call ends before the age decision. The second call satisfies the adult alternative.

Question 3

4 marks

Task X takes 7 seconds and task Y takes 3 seconds. They use fixed input and separate outputs. Task Z takes 2 seconds and needs both results. Identify the tasks that can overlap and explain why. Calculate sequential and ideal concurrent duration, and explain when Z may start.

Show solution and marking guidance

Indicative answer

X and Y can overlap because neither requires the other's result (1).
Sequential duration is 7 + 3 + 2 = 12 seconds (1).
Ideal concurrent duration is max(7, 3) + 2 = 9 seconds (1).
Z must wait until time 7 because it requires X as well as Y (1).
Assume adequate independent resources and no overhead.

Question 4

4 marks

Two concurrent tasks increment a shared completed-jobs counter. Explain how a lost update can occur, propose a control and state one tradeoff of that control.

Show solution and marking guidance

Indicative answer

Both tasks can read the same old value before either update completes (1), so one increment is overwritten and the total is too small (1).
Protect the complete read–modify–write with a lock, or use a suitable atomic increment (1).
Waiting for a lock/coordination adds overhead or reduces available overlap (1).
A lock on only the write does not protect the complete operation.

Specification links and scope

Checked against OCR H446 version 3.0 (2026): 2.1.4(a–c) covers decisions, conditions and flow; 2.1.5(a–b) covers overlapping parts and concurrency tradeoffs. The timeline has a text equivalent. Timings are illustrative, with their assumptions stated.

These are independently written explanations and practice questions. CompSciTutoring.co.uk is not affiliated with or endorsed by an examination board. The marking guidance is indicative; always check the syllabus for your examination year.

Found an error? Email a correction.

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Free A-Level Computer Science guide

Logical and concurrent thinking: decisions and dependencies

Write the condition that controls each decision, trace its effect on the next step and work out which tasks can overlap safely. Covers OCR A-Level H446 Paper 2 sections 2.1.4 and 2.1.5.

Content owner: Michael Print · Written for A-Level learners · Checked against official specifications

The short answer

Before you start

Recognise if/else and true/false values. Review the selection and loops guide for basic control flow. The timing examples use invented durations, so no concurrency library is needed.

By the end, you should be able to

Translate a rule using AND, OR and NOT with suitable brackets.
Trace which branch executes, including boundary inputs.
Identify independent tasks and tasks that depend on earlier results.
Evaluate a concurrency benefit alongside overhead or shared-state risks.

Translate the whole rule before choosing a branch

A visitor needs a ticket and must either be aged at least 16 or be accompanied by an adult. Treat all three inputs as already validated.

Translate each condition into a Boolean input

T: Has a ticket
A: Aged at least 16
G: Accompanied by an adult

The admission condition is T AND (A OR G). The OR gives two ways to satisfy the age/supervision part; AND makes the ticket compulsory in both cases.

Admission rule: T AND (A OR G), where 1 means true
T	A	G	A OR G	Admit
0	0	0	0	0
0	0	1	1	0
0	1	0	1	0
0	1	1	1	0
1	0	0	0	0
1	0	1	1	1
1	1	0	1	1
1	1	1	1	1

Worked example

Follow the decision points in order

Instead of returning only true/false, the centre wants a message explaining rejection. The first decision checks the ticket; the second decision is reached only after the visitor passes that check.

Complete activity-centre admission examplePython

def admission(has_ticket, age, with_adult):
    if not has_ticket:
        return "No ticket"
    elif age >= 16 or with_adult:
        return "Admit"
    else:
        return "Adult required"

print(admission(True, 16, False))
print(admission(True, 15, False))
print(admission(False, 15, True))

Ticket, age 16, no adult: not has_ticket is false. The second condition is true because 16 >= 16; output Admit.
Ticket, age 15, no adult: the ticket check passes, but both parts of the second condition are false; output Adult required.
No ticket, age 15, adult present: the first condition is true; output No ticket. The return ends this call, so the age/supervision decision is never reached.

The outputs are those three messages on separate lines. Test age 15 and 16 together: changing >= to > would wrongly reject the boundary case.

Draw the dependencies before overlapping tasks

A publishing tool receives a completed document. A produces its thumbnail; B builds its text index; C packages both results. A and B read fixed input and write separate outputs. C must wait for both.

Overlap independent work, then join the results

Illustrative timings: adequate independent resources and no coordination overhead. The worked example below adds that overhead.

Task dependencies and invented execution times
Task	Duration	Must wait for
A: thumbnail	6 seconds	Document ready
B: text index	4 seconds	Document ready
C: assemble package	2 seconds	A and B complete

Worked example

Calculate an overlap, then include its cost

Sequential execution: A, B and C take 6 + 4 + 2 = 12 seconds.
Ideal overlap: A and B start at time 0 on sufficient resources. B finishes at 4 seconds, but C still waits for A until time 6.
Join and finish: C runs from time 6 to time 8. The ideal total is max(6, 4) + 2 = 8 seconds.
Account for overhead: if starting and coordinating the tasks adds a further 1 second to this schedule, total time is 9 seconds. The saving over sequential execution is 3 seconds.

Evaluate what the tasks share

A lost update when two tasks share an unsafe counter
Step	Task A	Task B	Shared count
1	Reads 10		10
2		Reads 10	10
3	Writes 10 + 1		11
4		Writes 10 + 1	11

Both tasks intended to add one, but the final count is 11 instead of 12. This race condition makes correctness depend on the timing of shared operations.

Protect the whole read–modify–write operation with appropriate synchronisation. Protecting only the final write does not prevent the lost update.

Try it yourself

These four original questions total 15 marks. Solutions give indicative guidance, not an OCR mark scheme.

Question 1

4 marks

Show solution and marking guidance

Indicative answer

M AND (P OR V) (1 for requiring M, 1 for grouping the two alternatives).
With M = false, P = false, V = true, the intended condition is false (1), whereas (M AND P) OR V is true (1).
Accept an equivalent counterexample with M false and V true.

Question 2

3 marks

Using admission(), give the outputs of these calls in order: admission(False, 20, False), admission(True, 14, True), admission(True, 14, False).

Show solution and marking guidance

Indicative answer: No ticket (1); Admit (1); Adult required (1), in that order. The first call ends before the age decision. The second call satisfies the adult alternative.

Question 3

4 marks

Show solution and marking guidance

Indicative answer

X and Y can overlap because neither requires the other's result (1).
Sequential duration is 7 + 3 + 2 = 12 seconds (1).
Ideal concurrent duration is max(7, 3) + 2 = 9 seconds (1).
Z must wait until time 7 because it requires X as well as Y (1).
Assume adequate independent resources and no overhead.

Question 4

4 marks

Two concurrent tasks increment a shared completed-jobs counter. Explain how a lost update can occur, propose a control and state one tradeoff of that control.

Show solution and marking guidance

Indicative answer

Both tasks can read the same old value before either update completes (1), so one increment is overwritten and the total is too small (1).
Protect the complete read–modify–write with a lock, or use a suitable atomic increment (1).
Waiting for a lock/coordination adds overhead or reduces available overlap (1).
A lock on only the write does not protect the complete operation.

Specification links and scope

Found an error? Email a correction.

Need help applying this to unfamiliar questions?

Use the free examples first, then explore one-to-one tuition if guided practice would help.

Explore tuition Email Michael