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Course contents

  • How to Use This Course
  • Reading Paths
  • Glossary
  • Metrics Reference
  • Formal Cheat Sheet
  • Formal Foundations19
  • Properties and SVA16
  • Property Development and Constraints19
  • Proof Engines and Convergence23
  • Formal Applications20
  • Equivalence Checking14
  • Formal Coverage and Signoff15
  • Methodology and Debug13
  • Interview Prep15
  • Capstone: A Chip-Block Verification Lab24
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←Formal Verification
  1. Topics
  2. Formal Verification
  3. Reading Paths
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    Formal VerificationAll levels

    Reading Paths

    Three ordered routes through the Formal Verification course for a property writer, a formal owner and signoff lead, and an interview in two weeks, with a reason and an approximate time for every lesson.

    The course has 243 pages in ten sections, which is more than anyone needs for one goal. This page gives three routes. Each is an ordered table of the essential lessons with the reason to read it and an approximate time, so you can plan a week instead of guessing. Every route assumes you have read How to Use This Course. Essential means the lessons that carry the core path: read those in section order, and treat the rest as depth you add when a lesson leaves a question.

    How the times are built

    A lesson read once takes about 10 minutes. Lessons with a longer proof or a program to run are listed at 12 or 15. Working every proof, reading every counterexample and answering every check-yourself takes roughly two and a half times as long as reading. The course totals quoted on the hub come from the page text itself: about 971,000 characters of prose and tables read at about 1,000 characters a minute, and about 2,161,000 characters of code read at about 2,500 a minute, give about 31 hours to read. Adding 3 minutes for each of the 691 proof blocks (re-read its bug variant), 3 minutes for each of the 132 Python blocks, and 2 minutes for the check-yourself and exercise of each of the 243 pages gives about 80 hours with the proofs and exercises. These are planning estimates built from the lesson counts, not measurements of learners. Treat them as the size of the job, and expect the first few lessons to run slower while the design names settle.

    Section

    Pages

    Essential lessons

    Formal Foundations

    25

    Outcomes, assumptions, invariants, reset, cone, harness

    Properties and SVA

    21

    Monitor view, Boolean translation, implication, safety and liveness, mutation

    Property Development and Constraints

    25

    Spec to property, tracked items, assumption contract, data independence, assume-guarantee, checkers

    Proof Engines and Convergence

    30

    Reachability, BMC depth, induction and helpers, IC3 intuition, fairness and lassos, diagnosis

    Formal Applications

    27

    Connectivity, registers, deadlock and starvation, reset determinism, FIFO set

    Equivalence Checking

    19

    Miter, sequential equivalence, LEC assumptions, ECO flow

    Formal Coverage and Signoff

    20

    Antecedent covers, over-constraint, proof core, mutation, bound justification, checklist

    Methodology and Debug

    18

    Testplan, bring-up, slow-proof diagnosis, triage, regression

    Interview Prep

    20

    Framework, scenarios, rapid-fire, drills, spot-the-bug

    Capstone: A Chip-Block Verification Lab

    32

    Brief, four stages, solutions, appendix flow

    Route 1: property writer on a block

    You write RTL and want properties for it. This route takes the ideas a designer is missing: that a result is relative to its assumptions, that a property must be able to fail, and that the harness is part of the proof. It follows the course in section order, apart from the mutation check, which comes once you have properties and assumptions to test, and it ends with the capstone stage for your kind of block.

    Lesson

    Why you read it

    Minutes

    Three Outcomes of a Formal Run

    The vocabulary every later lesson uses.

    10

    State, Inputs and the Transition Relation

    The model every result is about: state, free inputs and one step.

    10

    A Proof Is Relative to Its Assumptions

    The same assertion proves, passes vacuously or fails with the assumption set.

    15

    Assume, Assert, Cover: the Three Roles

    What each directive means to the engine, and which side of a port each belongs on.

    10

    Free Initial State and the Reset Sequence

    The harness must create one reset sequence, or the proof starts anywhere.

    12

    Anatomy of a Formal Harness

    Parameters, free inputs, one reset, assumptions, assertions and covers in one place.

    12

    Reading a Result Report

    What each line of a result says, and what it leaves out.

    10

    What a Proof Engine Does with SVA

    An assertion is a small monitor added to the model.

    10

    Translating Textbook SVA to Boolean Past

    The translation table the rest of the course relies on.

    15

    Overlapped and Non-Overlapped in a Proof

    The most common off-by-one in review.

    10

    Antecedent: Every Cycle Versus Rose

    One attempt per cycle against one per edge.

    10

    Reading a Failing Assertion in a Trace

    From the failing cycle back to the attempt that started it.

    12

    Spec Sentence to Property

    Turn a requirement into a property that can fail.

    12

    Symbolic Constants and Tracked Items

    Data integrity without a scoreboard.

    12

    Assume Versus Assert by Side

    Assumed at the input that depends on it, asserted at the output that owes it.

    10

    The Assumption Review

    List, classify, discharge, and probe every assumption.

    12

    Checker Modules and Wrapper Harnesses

    Reuse a property set without hierarchical references.

    12

    Mutation Check of a Property

    A property is only as good as the bugs it kills.

    12

    Table-Driven Connectivity Proof

    Connectivity is a table, proved for all configurations.

    12

    Register Table to Properties

    The register table generates the property set.

    12

    W1C, Read-Only and Reset-Value Proofs

    The three register behaviours that hide bugs.

    12

    FIFO Ordering and Data Integrity

    The full property set of one design, with the depth each needs.

    12

    The Brief and Deliverables

    Start the capstone stage for your block.

    15

    Stage 1 FIFO Property Set

    Pick the stage lesson that matches your block: stage 1 for a FIFO or handshake.

    15

    Stage 2 CSR Proofs from the Table

    Stage 2 for a register block.

    15

    Stage 3 Pipeline Latency Properties

    Stage 3 for a pipeline.

    15

    After the capstone stage, return to any section whose lesson felt thin and read its topic hubs in order. The route is a spine, not the whole body.

    Route 2: formal owner and signoff lead

    You prove properties and defend the proofs. This route assumes route 1, or equivalent experience, for properties and assumptions, and concentrates on engines, convergence, applications, equivalence, coverage, the signoff evidence and the capstone that signs off all six designs.

    Lesson

    Why you read it

    Minutes

    BMC Unrolling by Hand

    What a bounded check is, as constraints.

    12

    COI Reduction Is Exact

    Why cutting to the cone changes no result.

    10

    Choosing a Depth

    Depth is derived, not guessed.

    12

    Base Case and Step

    A pass needs both, to the same k.

    12

    CTIs and Unreachable States

    Read a failing step and decide spurious or real.

    15

    Strengthening with Helper Invariants

    Exclude the unreachable region so the property turns inductive.

    12

    Diagnose Before You Tune

    Measure first then choose: reduce, split, strengthen.

    12

    Diagnosing a Slow Proof

    Measure cone, depth and engine progress before touching anything.

    12

    Lasso Counterexamples

    A liveness violation is an infinite trace that loops.

    12

    Deadlock, Livelock, Starvation Defined

    Three different failures that need three different checks.

    10

    Assume-Guarantee Contracts

    The rule that makes a split proof sound.

    12

    Circular Assume-Guarantee and the False Pass

    The one way a split proof lies.

    12

    Miter Construction

    Equivalence as a safety property on a miter.

    12

    pipe3 and Its Retimed Twin

    States differ, outputs agree: the cut invariant.

    12

    ECO Equivalence Flow

    Own a miter or an ECO: the flow and its intended differences.

    12

    Over-Constraint Seen Through Covers

    Activity covers expose a proof that is true by assumption.

    12

    Mutation-Based Formal Coverage

    The surviving mutants are your uncovered behaviour.

    12

    Justifying a Bound

    When a bounded result may carry signoff weight.

    12

    The Signoff Checklist in Full

    Every line of the package with its evidence.

    10

    Triage a Counterexample

    Decide in a fixed order: legal start, assumption, artefact, bug.

    12

    What Goes to Formal

    Choose the blocks and properties that earn a formal run.

    10

    Bring-Up Order

    Reset, harness, covers, then properties.

    10

    CI for Formal

    Per-commit and nightly sets, the ledger as the build output.

    10

    Stage 4 Induction on the Counter and FIFO Invariants

    The capstone stage that asks for helpers and a ledger across the designs.

    15

    Stage 4 Final Manifest and Review

    Review the whole ledger and call readiness.

    15

    Solutions: Ledger and Final Manifest

    Read it after your own attempt: the answers for the ledger and the final manifest.

    12

    Route 3: interview in two weeks

    Fourteen days, about half an hour a day (never more than 50 minutes). The plan adds the interview pages that test each subject, so some lessons are not on the other routes. Each day pairs the lessons that teach a subject with the interview-prep page that tests it. Say the answers aloud in the order assumption, mechanism, trade-off, evidence: an answer you only read is not yet an answer. If you have less time, keep days 1, 2, 3, 4, 5 and 10.

    Day

    Lesson

    Why you read it

    Minutes

    Day 1

    Scoring Rubric and Structure

    The answer shape the later days reuse.

    10

    Day 1

    Three Outcomes of a Formal Run

    Open with what a result means.

    10

    Day 2

    A Proof Is Relative to Its Assumptions

    The over-constraint story, with the trace.

    15

    Day 2

    Scenario: Everything Proves, Nothing Is Reached

    Everything proves and nothing is reached: find it.

    15

    Day 3

    Translating Textbook SVA to Boolean Past

    The forms interviewers quiz.

    15

    Day 3

    Whiteboard Questions 1 to 6

    Fast proof, assume versus assert, bounded pass, induction, FIFO, arbiter.

    25

    Day 4

    Base Case and Step

    Both obligations, same k.

    12

    Day 4

    CTIs and Unreachable States

    Spurious or real: the reading routine.

    15

    Day 5

    Strengthening with Helper Invariants

    How an invariant closes a step.

    12

    Day 5

    Rapid Fire: Induction and Bounded Proofs

    Depth, k, helpers, inconclusive.

    20

    Day 6

    Fairness, Weak and Strong

    Fairness constrains the environment only.

    12

    Day 6

    Bounded Response Is Safety

    Within N cycles is safety; eventually is liveness.

    12

    Day 7

    Arbiter Grant Latency Proof

    The window arithmetic for four requesters.

    12

    Day 7

    Scenario: A Deadlock-Like Trace in Arbiter and Fabric

    Cycle of waits against absence of progress.

    15

    Day 8

    Data Independence and Symbolic Tags

    When one tagged bit stands for all data.

    12

    Day 8

    What LEC Assumes

    One-to-one states, scan off, consistent constants.

    10

    Day 9

    Miter Construction

    The miter question, with the mismatch read.

    12

    Day 9

    Scenario: A Late ECO Breaks Equivalence

    Setup difference against real difference.

    15

    Day 10

    Antecedent Covers and Witness Traces

    Every implication gets a cover.

    10

    Day 10

    The Signoff Checklist in Full

    The evidence behind a signoff claim.

    10

    Day 11

    Whiteboard Questions 7 to 12

    Triage, memory, disable-iff, equivalence, wrong tool, signoff.

    25

    Day 11

    Scenario: A Proof That Will Not Converge

    Diagnose under deadline, report honestly.

    15

    Day 12

    Numeric Drills: State and Depth

    Practise the arithmetic aloud.

    25

    Day 12

    Numeric Drills: Engine and Assumption Load

    Cones, lassos, clauses, assumption share.

    25

    Day 13

    Spot the Bug in the Property Answers

    Six flawed answers, each with the defect named.

    20

    Day 13

    Spot the Bug in the Proof Claims

    Six flawed claims, each corrected.

    20

    Day 14

    Stage 4 Final Manifest and Review

    Review the whole ledger and call readiness.

    15

    Do not memorise design numbers as if they were typical of real blocks. They are teaching values chosen so the proofs are checkable. What an interviewer wants is the method: the outcome vocabulary, the assumption list, and which evidence supports the claim.

    Check yourself You have three days, not two weeks. What do you keep from route 3 and what do you give up?

    Keep the framework and the first whiteboard set, since they train the answer shape, plus one subject day each on assumptions, induction and signoff. Give up the rapid-fire pages and the scenario days, which reward breadth you cannot build in three days.

    Related topics

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    • How to Use This Course

    • Glossary

    • Formal Cheat Sheet

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    See also

    • Metrics Reference
    • Formal Cheat Sheet
    • Formal Foundations