# Equivalence checking

## What is equivalence checking in formal verification?

Definition. Equivalence checking is a portion of a larger discipline called formal verification. This technology uses mathematical modeling techniques to prove that two representations of design exhibit the same behavior.

## How do you verify equivalence?

1:503:22How to Verify the Logical Equivalence using the Laws of Logic – YouTubeYouTubeStart of suggested clipEnd of suggested clipWhich is the same as q and not q in any case this statement is a contradiction. So this is p or andMoreWhich is the same as q and not q in any case this statement is a contradiction. So this is p or and i’m just going to put a little c here where c denotes. Contradiction.

## What is LEC check?

LEC (Logic Equivalence Check) is the essential step to ensure the functional check between RTL and netlist as can also be depicted from the Fig. 1. Many EDA companies provide tools to do the check.

## What is the need of type equivalence checking?

The major advantage of name equivalence checking is that it is efficient. The check involves ensuring that two types have the same declaration, which can be reduced to a single word comparison in most machines. This advantage goes a long way to explaining the popularity of the scheme within many programming languages.

## What equivalence means?

Definition of equivalence 1a : the state or property of being equivalent. b : the relation holding between two statements if they are either both true or both false so that to affirm one and to deny the other would result in a contradiction. 2 : a presentation of terms as equivalent.

## What are equivalence rules?

Recall that two propositions are logically equivalent if and only if they entail each other. In other words, equivalent propositions have the same truth value in all possible circumstances: whenever one is true, so is the other; and whenever one is false, so is the other.

## What is difference between LVS and LEC?

LEC and LVS are checks used in different stages of physical design to ascertain the functionality and layout sanity respectively. Both are done at different phases of the PNR flow. LEC starts as early as the front end and goes on till the final tape-out phase whereas LVS is primarily a backend sanity check.

## What is formality check in VLSI?

Formality® is an equivalence-checking (EC) solution that uses formal, static techniques to determine if two versions of a design are functionally equivalent. Formality delivers capabilities for ECO assistance and advanced debugging to help guide the user in implementing and verifying ECOs.

## What is abort points in LEC?

2.2 Dealing with Abort Points A common issue that all LEC users must face is Abort points, cases where the tool is unable to complete verification of some points due to lack of computing power.

## What is type Equivalence?

TYPE CHECKING RULES usually have the form if two type expressions are equivalent then return a given type else return type_error. KEY IDEAS. The central issue is then that we have to define when two given type expressions are equivalent.

## What is the difference between type Equivalence and type compatibility?

In the type equivalence objects and contexts can only be identical if they are of the same form where as type compatibility determines the what information is stored inside the object that are based on the level of compatibility.

## What are the types of type conversion?

There are two types of conversion: implicit and explicit. The term for implicit type conversion is coercion. Explicit type conversion in some specific way is known as casting.

## What is functional equivalence?

In ecology, functional equivalence (or functional redundancy) is the ecological phenomena that multiple species representing a variety of taxonomic groups can share similar, if not identical, roles in ecosystem functionality (e.g., nitrogen fixers, algae scrapers, scavengers).

## What is formality check in VLSI?

Formality® is an equivalence-checking (EC) solution that uses formal, static techniques to determine if two versions of a design are functionally equivalent. Formality delivers capabilities for ECO assistance and advanced debugging to help guide the user in implementing and verifying ECOs.

## What is Conformal LEC?

Conformal Smart LEC. Massively parallel architecture and adaptive-proof technology deliver. turnaround time improvement. Cadence® Conformal® Smart Logic Equivalence Checker (LEC) is the next-generation equivalence checking solution.

## What is conformal in VLSI?

It surrounds a particular layer which can be either conductor or other dielectric. It means, it is not a general dielectric layer which can present anywhere. You can find it (conformal layer) only at place where it’s corresponding layer present. Like POLY, M1 , M2 etc.

## What is equivalence checking?

Equivalence checking, that is, determining when two (infinite-state) systems are in some semantic sense equal, is clearly a particularly relevant problem in system verification. Indeed, such questions have a long tradition in the field of (theoretical) computer science. Since the proof by Moore [121] in 1956 of the decidability of language equivalence for finite-state automata, formal language theorists have been studying the equivalence problem over classes of automata which express languages which are more expressive than the class of regular languages generated by finite-state automata. Bar-Hillel, Perles and Shamir [ 6] were the first to demonstrate, in 1961, that the class of languages defined by context-free grammars was too wide to admit a decidable theory for language equivalence. Shortly after this, Korenjak and Hopcroft [ 95] demonstrated that language equivalence between simple (deterministic) grammars is decidable. Only recently has the long-open problem of language equivalence between deterministic push-down automata (DPDA) been settled (positively) by SéAnizergues [ 132, 133 ].

## What is the most efficient way to prove equivalence?

If your design is comprised of simple combinational logic, or if there is a state-matching relation between the flops across two models you want to compare (as is the case when netlists are generated by most synthesis tools), a combinational FEV tool will probably be the most efficient way to prove equivalence.

## What is FEV in chip design?

This is the primary FEV technique used for state-matching models, where every state element (latch or flop) in the SPEC corresponds to a specific state element in the IMP. In this mode, two designs are claimed to be equivalent when all combinational logic between any pair of corresponding states are logically equivalent. In other words, there is a 1:1 correspondence between the state elements of the two models. Whenever the equivalence of a pair of state elements in the two models is checked, the tool uses the assumption that corresponding state elements in their fanin cones will contain identical values at all points in time. In effect, every latch or flop in the two designs is being treated as a cut point, with verification only encompassing the logic between the state elements.

## What is sequential equivalence?

Sequential equivalence is also referred to as cycle-accurate equivalence by some vendors. With sequential FEV tools, we ask the question of whether two models will ultimately generate the same outputs at the same times based on an equivalent set of inputs, without requiring that internal state elements fully correspond. Thus, sequential FEV tools can handle cases like the recoded FSM described above.

## How does PBCOV work?

PBCOV runs the test suite T against Si and computes Pcover the set of covered states. PBCOV uses equivalence checking techniques in model checking tools such as ABC [40] to compute the difference between Psym and Pcover. Then PBCOV checks the feasibility of each smiss state from Psym − Pcover against S sym ⇒ P sym using a satisfiability modulo theory solver such as Yices [41]. If the solver returns an inconclusive result, then PBCOV over approximates Ssym by using a min-cut-based program slicing technique. The overapproximation computes a cut in the control flow diagram corresponding to Ssym and considers the variables crossing the cut as free variables. This is an overapproximation since the free variables may assume values that are not feasible. In case the solver returns a satisfiable result, the result could be used as an additional test case and smiss is included in the metric. In case the solver returns an unsatisfiable result, then smiss is deemed unreachable and is not used in the denominator of the metric.

## When was the decidability of language equivalence for finite-state automata discovered?

Since the proof by Moore [121] in 1956 of the decidability of language equivalence for finite-state automata, formal language theorists have been studying the equivalence problem over classes of automata which express languages which are more expressive than the class of regular languages generated by finite-state automata.

## When to use sequential FEV?

If you have both FPV and sequential FEV tools available, you should usually use the sequential FEV tools when trying to solve a non-state-matching model equivalence problem.

## What is a formal equivalence check?

A formal equivalence check can be performed between any two representations of a design: RTL <> netlist, netlist <> netlist or RTL <> RTL, though the latter is rare compared to the first two. Typically, a formal equivalence checking tool will also indicate with great precision at which point there exists a difference between two representations.

## What is sequence equivalence checking?

Sequential Equivalence Checking: Sometimes, two machines are completely different at the combinational level, but should give the same outputs if given the same inputs. The classic example is two identical state machines with different encodings for the states. Since this cannot be reduced to a combinational problem, more general techniques are required.

## What is machine equivalence?

The most common approach is to consider the problem of machine equivalence which defines two synchronous design specifications functionally equivalent if, clock by clock, they produce exactly the same sequence of output signals for any valid sequence of input signals.

## What is the role of logical equivalence check?

With shrinking technology nodes and increasing complexity, logical equivalence check plays a major role in ensuring the correctness of the functionality.

## Why are all the endpoints of a connection reported as non-equivalent?

The reason behind is that many paths which are going through one failed/broken connection – and hence all its endpoints (compare points) – are reported “Non-equivalent”.

## What are the EDA tools for LEC?

There are various EDA tools for performing LEC, such as Synopsys Formality and Cadence Conformal. We are considering Conformal tool as a reference for the purpose of explaining the importance of LEC.

## When to use no name mapping?

Conversely, the no-name-mapping method is useful when the Conformal tool must map designs with completely different names. By default, it automatically maps key points with the name-first mapping method when it exits the setup mode. The key points that the Conformal tool does not map are classified as unmapped points.

## Does clock gating get mapped after cloning?

Clock gating cells not getting mapped after cloning in revised netlist.

## Can conformal tool continue comparison?

Thus, the Conformal tool can continue the comparison on only the aborted compare points. The Conformal tool displays the completed run time and total memory used for the comparison.

## What is the role of logical equivalence check?

With shrinking technology nodes and increasing complexity, logical equivalence check plays a major role in ensuring the correctness of the functionality.

## Why are all the endpoints of a connection reported as non-equivalent?

The reason behind is that many paths which are going through one failed/broken connection – and hence all its endpoints (compare points) – are reported “Non-equivalent”.

## What is the conformal tool?

During the second phase of equivalence checking, the Conformal tool automatically maps key points and compares them. When the comparison is complete, it pinpoints the differences. The Conformal tool employs two name-based methods and one no-name method to map key points. Name-based mapping is useful for gate-to-gate comparisons when minor changes have been made to the logic.

## What are the EDA tools for LEC?

There are various EDA tools for performing LEC, such as Synopsys Formality and Cadence Conformal. We are considering Conformal tool as a reference for the purpose of explaining the importance of LEC.

## When to use no name mapping?

Conversely, the no-name-mapping method is useful when the Conformal tool must map designs with completely different names. By default, it automatically maps key points with the name-first mapping method when it exits the setup mode. The key points that the Conformal tool does not map are classified as unmapped points.

## Is logical equivalence check failure uncommon?

It is not uncommon for teams to encounter logical equivalence check (LEC) failure. This paper gives an introduction of logical equivalence check, flow setup, steps to debug it, and solutions to fix LEC.

## Does clock gating get mapped after cloning?

Clock gating cells not getting mapped after cloning in revised netlist.

In this course, you learn to use the Conformal ® Equivalence Checker to perform functional verification. You learn the basic flow of equivalence checking and how to run hierarchical comparison of designs. The lab exercises follow major topics and are designed to be directly applicable in design and design verification.

## Learning Objectives

Use Conformal logic equivalence checking for flat and hierarchical design comparison

## Related Courses

Please see course learning maps at this link for a visual representation of courses and course relationships. Regional course catalogs may be viewed here.

## Overview

Formal equivalence checking process is a part of electronic design automation (EDA), commonly used during the development of digital integrated circuits, to formally prove that two representations of a circuit design exhibit exactly the same behavior.

## Equivalence checking and levels of abstraction

In general, there is a wide range of possible definitions of functional equivalence covering comparisons between different levels of abstraction and varying granularity of timing details.
• The most common approach is to consider the problem of machine equivalence which defines two synchronous design specifications functionally equivalent if, clock by clock, they produce exactly the same sequence of output signals for any valid sequence of input signals.

## Synchronous machine equivalence

The register transfer level (RTL) behavior of a digital chip is usually described with a hardware description language, such as Verilog or VHDL. This description is the golden reference model that describes in detail which operations will be executed during which clock cycle and by which pieces of hardware. Once the logic designers, by simulations and other verification methods, have verified register transfer description, the design is usually converted into a netlist by a logic synth…

## Methods

There are two basic technologies used for boolean reasoning in equivalence checking programs:
• Binary decision diagrams, or BDDs: A specialized data structure designed to support reasoning about boolean functions. BDDs have become highly popular because of their efficiency and versatility.
• Conjunctive Normal Form Satisfiability: SAT solvers returns an assignment to the variables of a propositional formula that satisfies it if such an assignment exists. Almost any …

There are two basic technologies used for boolean reasoning in equivalence checking programs:
• Binary decision diagrams, or BDDs: A specialized data structure designed to support reasoning about boolean functions. BDDs have become highly popular because of their efficiency and versatility.
• Conjunctive Normal Form Satisfiability: SAT solvers returns an assignment to the variables of a propositional formula that satisfies it if such an assignment exists. Almost any boo…

## Commercial applications for equivalence checking

Major products in the Logic Equivalence Checking (LEC) area of EDA are:
• FormalPro by Mentor Graphics
• Questa SLEC by Mentor Graphics

## Generalizations

• Equivalence Checking of Retimed Circuits: Sometimes it is helpful to move logic from one side of a register to another, and this complicates the checking problem.
• Sequential Equivalence Checking: Sometimes, two machines are completely different at the combinational level, but should give the same outputs if given the same inputs. The classic example is two identical state machines with different encodings for the states. Since this cannot be reduced to a combination…