Equivalence Checking: Equivalence checking is a formal technique used in logic synthesis and verification to determine if two formal statements are equivale...
Equivalence Checking: Equivalence checking is a formal technique used in logic synthesis and verification to determine if two formal statements are equivalent or "logically equivalent". It involves constructing a new, equivalent statement from the original statements using a set of rules and operations.
Combinational Equivalence:
Two statements are combinatorially equivalent if they can be combined together using a combination operator (like AND, OR, etc.) in a way that preserves the truth values of both statements.
For example: (p AND q) ∨ (r AND s) is equivalent to (p ∨ r) AND (q ∨ s).
Sequential Equivalence:
Two statements are sequentially equivalent if they can be derived from each other using a sequence of logical axioms.
For example: p -> q and q -> r implies p -> r.
Equivalence Checking Process:
Equivalence checking typically involves the following steps:
Start with the original statements.
Use logical axioms and rules to manipulate them into equivalent forms.
If possible, simplify the resulting statements to obtain a single, equivalent statement.
If the equivalence is established, the original statements are equivalent.
Equivalence Checking in Logic Synthesis and Verification:
Equivalence checking is a crucial step in formal verification.
It helps in proving the correctness of logical systems and formal expressions by demonstrating that they are equivalent to simpler, equivalent statements.
Equivalence checking is also used in synthesis to construct new statements that are equivalent to existing ones.
Examples:
(p AND q) ∨ (r AND s) is equivalent to (p ∨ r) AND (q ∨ s).
p -> q and q -> r implies p -> r.
(p AND q) ∨ (r AND s) is equivalent to (p ∨ r) AND (q ∨ s)