Available expressions analysis in Compiler Design - Practice Problems & Coding Challenges

Challenge - 5 Problems

🧠 Conceptual

intermediate

Understanding the purpose of available expressions analysis

What is the main goal of performing available expressions analysis in compiler design?

A To find expressions that have been computed and not modified on all paths to a program point

B To identify variables that are never used in the program

C To detect unreachable code segments in the program

D To determine the maximum number of loops nested in the program

💡 Hint

Think about expressions that can be reused without recomputation.

Available expressions analysis finds expressions that have already been computed and whose operands have not changed along all paths to a point, enabling optimization by reusing these expressions.

📋 Factual

intermediate

Data flow direction in available expressions analysis

In which direction is the data flow analysis performed for available expressions?

A Backward, from program end to start

B Forward, from program start to end

C Both forward and backward simultaneously

D Random order, depending on control flow

💡 Hint

Consider when expressions become available during execution.

Available expressions analysis is a forward data flow analysis because it tracks expressions computed as the program executes from start to end.

🔍 Analysis

advanced

Effect of assignment on available expressions

Given the statement x = y + z, which of the following expressions becomes unavailable immediately after this statement?

A All expressions containing <code>y</code> or <code>z</code>

B Only the expression <code>y + z</code>

C Any expression containing variable <code>x</code>

D No expressions become unavailable

💡 Hint

Think about how changing a variable affects expressions that use it.

Assigning to x changes its value, so any expression involving x may no longer be valid and thus becomes unavailable.

❓ Comparison

advanced

Difference between available expressions and reaching definitions

Which statement correctly distinguishes available expressions analysis from reaching definitions analysis?

A Available expressions are a backward analysis; reaching definitions are forward

B Available expressions track variable assignments; reaching definitions track expression computations

C Both analyses track the same information but use different algorithms

D Available expressions track computed expressions not invalidated; reaching definitions track where variables are assigned

💡 Hint

Consider what each analysis is trying to find about the program.

Available expressions analysis finds expressions computed and still valid; reaching definitions analysis finds where variables get their current values assigned.

❓ Reasoning

expert

Available expressions at a control flow join point

At a program point where two control flow paths join, how is the set of available expressions determined?

A By intersecting the sets of available expressions from both paths

B By taking the union of the sets of available expressions from both paths

C By taking the set from the path with more expressions available

D By discarding all expressions and starting fresh

💡 Hint

Think about which expressions are guaranteed to be available regardless of the path taken.

Only expressions available on all incoming paths are considered available at the join point, so the intersection of sets is used.

Practice

1. What is the main purpose of available expressions analysis in compiler design?

easy

A. To find expressions that have already been computed and not changed

B. To detect syntax errors in the source code

C. To allocate memory for variables

D. To generate machine code from source code

Solution

1. Step 1: Understand the goal of available expressions analysis

   This analysis identifies expressions that have been computed before and whose values have not changed since.

2. Step 2: Compare with other compiler tasks

   Unlike syntax checking or code generation, available expressions focus on optimization by reusing computed values.

3. Final Answer:

   To find expressions that have already been computed and not changed -> Option A

4. Quick Check:

   Available expressions = computed and unchanged expressions [OK]

Hint: Focus on expressions reused without recomputation [OK]

Common Mistakes:

• Confusing with syntax error detection
• Thinking it allocates memory
• Mixing with code generation tasks

2. Which of the following correctly represents the GEN set in available expressions analysis?

easy

A. All variables used in the program

B. Variables assigned new values in a block

C. Expressions computed in a block and not killed within it

D. Expressions that are never computed in the program

Solution

1. Step 1: Define the GEN set

   GEN set contains expressions that are computed in a block and remain valid (not overwritten) within that block.

2. Step 2: Eliminate incorrect options

   Variables assigned new values relate to KILL sets, not GEN. Expressions never computed or all variables are unrelated.

3. Final Answer:

   Expressions computed in a block and not killed within it -> Option C

4. Quick Check:

   GEN = computed and valid expressions [OK]

Hint: GEN = expressions generated and still valid in block [OK]

Common Mistakes:

• Mixing GEN with KILL sets
• Confusing variables with expressions
• Selecting unrelated program elements

3. Consider a basic block with the following statements:

a = b + c
d = a + e
b = 5

Which expressions are available at the end of this block?

medium

A. {a + e}

B. {} (empty set)

C. {b + c, a + e}

D. {b + c}

Solution

1. Step 1: Identify expressions computed

   The expressions computed are b + c and a + e.

2. Step 2: Check if expressions remain valid

   b + c is killed because b is assigned later (b = 5). a + e remains available since neither a nor e is reassigned after its computation.

3. Final Answer:

   {a + e} -> Option A

4. Quick Check:

   Expressions available if no operand reassigned after computation [OK]

Hint: Check operand reassignments after each computation [OK]

Common Mistakes:

• Ignoring variable reassignment kills expressions
• Assuming all computed expressions remain available
• Confusing direct operands with transitive dependencies

4. Identify the error in this available expressions analysis step:

GEN = {x + y}
KILL = {x = 3}
Available expressions at block end = GEN ∪ (IN - KILL)

What is wrong with this calculation?

medium

A. Using union (∪) instead of intersection (∩) for available expressions

B. Confusing KILL set with GEN set

C. Not updating IN set before calculation

D. Including variables instead of expressions in KILL

Solution

1. Step 1: Recall available expressions formula

   The formula Available_out = GEN ∪ (IN - KILL) is correct when GEN and KILL contain expressions.

2. Step 2: Identify the error in the sets

   KILL = {x = 3} includes an assignment instead of killed expressions (e.g., those with x as operand).

3. Final Answer:

   Including variables instead of expressions in KILL -> Option D

4. Quick Check:

   KILL = expressions killed by assignments [OK]

Hint: KILL contains killed expressions, not assignments [OK]

Common Mistakes:

• Misrepresenting KILL set contents
• Mixing variables and expressions in sets
• Ignoring proper IN set update

5. Given two basic blocks with:

Block 1: GEN = {a + b}, KILL = {a = 4}
Block 2: GEN = {a + b, c + d}, KILL = {b = 2}

If the IN set for Block 2 is {a + b}, what is the OUT set for Block 2 after available expressions analysis?

hard

A. {a + b, c + d}

B. {c + d}

C. {a + b}

D. {} (empty set)

Solution

1. Step 1: Calculate OUT set formula

   OUT = GEN ∪ (IN ∩ ¬KILL). Here, GEN = {a + b, c + d}, IN = {a + b}, KILL kills expressions involving b.

2. Step 2: Remove killed expressions from IN

   a + b is killed (involves b), so IN ∩ ¬KILL = {}.

3. Step 3: Compute OUT set

   OUT = GEN ∪ {} = {a + b, c + d}, but since a + b is killed by KILL, it should not be in OUT. Therefore, OUT = {c + d}.

4. Final Answer:

   {c + d} -> Option B

5. Quick Check:

   OUT = GEN ∪ (filtered IN) with killed expressions removed [OK]

Hint: Filter IN with ¬KILL, then union GEN [OK]

Common Mistakes:

• Applying KILL to GEN expressions
• Not intersecting IN with complement of KILL
• Assuming all GEN expressions remain available