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ABC: An Industrial-Strength Academic Synthesis and Verification Tool (based on a tutorial given at CAV 2010)


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Title: ABC: An Industrial-Strength Academic Synthesis and Verification Tool (based on a tutorial given at CAV 2010)

ABC An Industrial-Strength Academic Synthesis
and Verification Tool(based on a tutorial given
at CAV 2010)
  • Berkeley Verification and Synthesis Research
  • UC Berkeley
  • Robert Brayton, Niklas Een, Alan Mishchenko
  • Jiang Long, Sayak Ray, Baruch Sterin
  • Thanks to NSA, SRC, and industrial sponsors,
  • Actel, Altera, Atrenta, IBM, Intel, Jasper,
    Magma, Oasys,
  • Real Intent, Synopsys, Tabula, and Verific

  • What is ABC?
  • Synthesis/verification synergy
  • Introduction to AIGs
  • Representative transformations
  • Integrated verification flow
  • Verification example
  • Future work

A Plethora of ABCs
  • http//
  • ABC (American Broadcasting Company)
  • A television network
  • ABC (Active Body Control)
  • ABC is designed to minimize body roll in corner,
    accelerating, and braking. The system uses 13
    sensors which monitor body movement to supply the
    computer with information every 10 ms
  • ABC (Abstract Base Class)
  • In C, these are generic classes at the base of
    the inheritance tree objects of such abstract
    classes cannot be created
  • Atanasoff-Berry Computer
  • The AtanasoffBerry Computer (ABC) was the first
    electronic digital computing device. Conceived in
    1937, the machine was not programmable, being
    designed only to solve systems of linear
    equations. It was successfully tested in 1942.
  • ABC (supposed to mean as simple as ABC)
  • A system for sequential synthesis and
    verification at Berkeley

  • Started 6 years ago as a replacement for SIS
  • Academic public-domain tool
  • Industrial-strength
  • Focuses on efficient implementation
  • Has been employed in commercial offerings of
    several CAD companies
  • Exploits the synergy between synthesis and

Design Flow
Property Checking
System Specification
Logic synthesis
Technology mapping
Physical synthesis
Synthesis and Verification
  • Synthesis
  • Given a Boolean function
  • Represented by a truth table, BDD, or a circuit
  • Derive a good circuit implementing it
  • Verification
  • Given a (very large) circuit
  • Prove that its output is always constant

Synthesis/Verification Synergy
  • Similar solutions
  • e.g. retiming in synthesis / retiming in
  • Algorithm migration
  • e.g. BDDs, SAT, induction, interpolation,
  • Related complexity
  • scalable synthesis ltgt scalable verification
  • Common data-structures
  • combinational and sequential AIGs

Areas Addressed by ABC
  • Combinational synthesis
  • AIG rewriting
  • technology mapping
  • resynthesis after mapping
  • Sequential synthesis
  • retiming
  • structural register sweep
  • merging seq. equiv. nodes
  • Combinational verification
  • SAT solving
  • SAT sweeping
  • combinational equivalence checking (CEC)
  • Sequential verification
  • bounded model checking (BMC)
  • unbounded model/equiv checking (MC/EC)
  • safety/liveness properties
  • exploits synthesis history

  • Logic function (e.g. F abcd)
  • Variables (e.g. b)
  • Minterms (e.g. abcd)
  • Cube (e.g. ab)
  • Logic network
  • Primary inputs/outputs
  • Logic nodes
  • Fanins/fanouts
  • Transitive fanin/fanout cone
  • Cut and window (defined later)

AIG (And-Inverter Graphs) Definition and Examples
AIG is a Boolean network composed of two-input
ANDs and inverters
cdab 00 01 11 10
00 0 0 1 0
01 0 0 1 1
11 0 1 1 0
10 0 0 1 0
F(a,b,c,d) ab d(acbc)
6 nodes 4 levels
F(a,b,c,d) ac(bd) c(ad) ac(bd)
cdab 00 01 11 10
00 0 0 1 0
01 0 0 1 1
11 0 1 1 0
10 0 0 1 0
7 nodes 3 levels
Structural Hashing
  • Propagates constants and merges structural
  • Is applied on-the-fly during AIG construction
  • Results in circuit compaction

Example F abc G (abc) H abc
Before structural hashing
After structural hashing
Why AIGs?
  • Same reasons hold for both synthesis and
  • Easy to construct, relatively compact, robust
  • 1M AIG 12Mb RAM
  • Can be efficiently stored on disk
  • 3-4 bytes / AIG node (1M AIG 4Mb file)
  • Unifying representation
  • Used by all the different verification engines
  • Easy to pass around, duplicate, save
  • Compatible with SAT solvers
  • Efficient AIG-to-CNF conversion available
  • Circuit-based SAT solvers work directly on AIG
  • AIGs simulation SAT works well in many

AIG Memory Usage
  • Fixed amount of memory for each node
  • Can be done by a simple custom memory manager
  • Dynamic fanout manipulation is supported!
  • Allocate memory for nodes in a topological order
  • Optimized for traversal in the same topological
  • Mostly AIG can be stored in cache fewer cache
  • Small static memory footprint in many
  • Compute fanout information on demand

Classical Logic Synthesis
Equivalent AIG in ABC
AIG is a Boolean network of 2-input AND nodes and
invertors (dotted lines)
One AIG Node Many Cuts
Combinational AIG
  • Each AIG cut represents a different logic node
  • AIG manipulation with cuts is equivalent to
    working on many Boolean networks at the same time

Different cuts for the same node
Combinational Synthesis
  • AIG rewriting minimizes the number of AIG nodes
    without increasing the number of AIG levels

Rewriting AIG subgraphs
  • Pre-computing AIG subgraphs
  • Consider function f abc

Rewriting node A
Rewriting node B
In both cases 1 node is saved
Combinational Rewriting
  • iterate 10 times
  • for each AIG node
  • for each k-cut
  • derive node output as function of cut
  • if ( smaller AIG is in the
    pre-computed library )
  • rewrite using improved AIG

Note For 4-cuts, each AIG node has, on average,
5 cuts compared to a SIS node with only 1
cut Rewriting at a node can be very fast using
hash-table lookups, truth table manipulation,
disjoint decomposition
  • Resubstitution means expressing one function in
    terms of others
  • Given f(x) and gi(x), is it possible to express
    f in terms of a subset of functions gi?
  • If so, what is function f(g)?
  • An efficient truth-table-based and SAT-based
    solution exists
  • Runs in seconds for functions with hundreds of
  • A. Mishchenko, R. Brayton, J.-H. R. Jiang, and S.
    Jang, "Scalable don't care based logic
    optimization and resynthesis", Proc. FPGA'09.

Technology Mapping
Input A Boolean network (And-Inverter Graph)
Output A netlist of K-LUTs implementing AIG and
optimizing some cost function
Technology Mapping
The subject graph
The mapped netlist
Library Formats for Tech Mapping
  • GENLIB format
  • Simple format used in academic tools
  • For each gate, lists its name, Boolean function,
    pin names and order, area, pin-to-pin delays, etc
  • http//
  • LIBERTY format
  • Elaborate format used in industrial tools
  • For each gate, represents all information needed
    for synthesis, mapping, delay/power computation,
  • http//
  • ABC reads both formats but uses only a subset of
    available information

Comparison of Two Syntheses
  • Classical synthesis
  • Boolean network
  • Network manipulation (algebraic)
  • Elimination
  • Decomposition (common kernel extraction)
  • Node minimization
  • Espresso
  • Dont cares computed using BDDs
  • Resubstitution
  • Contemporary synthesis
  • AIG network
  • DAG-aware AIG rewriting (Boolean)
  • Several related algorithms
  • Rewriting
  • Refactoring
  • Balancing
  • Node minimization
  • Boolean decomposition
  • Dont cares computed using simulation and SAT
  • Resubstitution with dont cares

Note here all algorithms are scalable no SOP,
no BDDs, no Espresso
Formal Verification
  • Property checking
  • Create miter from the design and the safety
  • Special construction for liveness
  • Biere et al, Proc. FMICS06
  • Equivalence checking
  • Create miter from two versions of the same design
  • Assuming the initial state is given
  • The goal is to prove that the output of the miter
    is 0, for all states reachable from the initial.

Outcomes of Verification
  • Success
  • The property holds in all reachable states
  • Failure
  • A finite-length counter-example (CEX) is found
  • Undecided
  • A limit on resources (such as runtime) is reached

Inductive Invariant
  • An inductive invariant is a Boolean function in
    terms of register variables, such that
  • It is true for the initial state(s)
  • It is inductive
  • assuming that is holds in one (or more)
    time-frames allows us to prove it in the next
  • It does not contain bad states where the
    property fails

State space
Inductive Invariant (cont.)
  • It does not matter how inductive invariant is
  • If it is available in any form (as a circuit, BDD
    or CNF), it can be checked for correctness
    using a third-party tool
  • This way, verification proof can be certified
  • Comment 1 If the property is true, the set of
    all reachable states is an inductive invariant
  • Comment 2 In practice, computing the set of all
    reachable states is often impossible.
  • In such cases, an inductive invariant is an
    over-approximation of reachable states.

Verification Engines
  • Bug-hunters
  • random simulation
  • bounded model checking (BMC)
  • hybrids of the above two (semi-formal)
  • Provers
  • K-step induction, with or without uniqueness
  • BDDs (exact reachability)
  • Interpolation (over-approximate reachability)
  • Property directed reachability (over-approximate
  • Transformers
  • Combinational synthesis
  • Reparameterization
  • Retiming

Integrated Verification Flow
  • Preprocessing
  • Creating a miter
  • Computing the intial state, etc
  • Handling combinational problems
  • Handling sequential problems
  • Start with faster engines
  • Continue with slower engines
  • Run main induction loop
  • Call last-gasp engines

Command dprove in ABC
  • transforming initial state (undc, zero)
  • converting into an AIG (strash)
  • creating sequential miter (miter -c)
  • combinational equivalence checking (iprove)
  • bounded model checking (bmc)
  • sequential sweep (scl)
  • phase-abstraction (phase)
  • most forward retiming (dret -f)
  • partitioned register correspondence (lcorr)
  • min-register retiming (dretime)
  • combinational SAT sweeping (fraig)
  • for ( K 1 K ? 16 K K 2 )
  • signal correspondence (scorr)
  • stronger AIG rewriting (dc2)
  • min-register retiming (dretime)
  • sequential AIG simulation
  • interpolation (int)
  • BDD-based reachability (reach)
  • saving reduced hard miter (write_aiger)

Combinational solver
Faster engines
Slower engines
Main induction loop
Last-gasp engines
Typical Run of SEC in ABC
  • abc - gt miter cm r\orig\s38584.1.blif
  • abc - gt dprove vb
  • Original miter Latches 4162. Nodes
  • Sequential cleanup Latches 3777. Nodes
    22081. Time 0.07 sec
  • Forward retiming Latches 5196. Nodes
    21743. Time 0.24 sec
  • Latch-corr (I 15) Latches 4311. Nodes
    19670. Time 2.88 sec
  • Fraiging Latches 4311. Nodes
    18872. Time 0.35 sec
  • Min-reg retiming Latches 2280. Nodes
    18867. Time 0.93 sec
  • K-step (K 1,I 8) Latches 2053. Nodes
    16602. Time 13.19 sec
  • Min-reg retiming Latches 2036. Nodes
    16518. Time 0.14 sec
  • Rewriting Latches 2036. Nodes
    14399. Time 1.64 sec
  • Seq simulation Latches 2036. Nodes
    14399. Time 0.29 sec
  • K-step (K 2,I 9) Latches 1517. Nodes
    10725. Time 14.81 sec
  • Min-reg retiming Latches 1516. Nodes
    10725. Time 0.14 sec
  • Rewriting Latches 1516. Nodes
    10498. Time 1.09 sec
  • Seq simulation Latches 1516. Nodes
    10498. Time 0.45 sec
  • K-step (K 4,I 8) Latches 0. Nodes
    0. Time 11.89 sec

Combinational Equivalence Checking (command
  • Naïve approach
  • Build output miter call SAT
  • works well for many easy problems
  • Better approach - SAT sweeping
  • based on incremental SAT solving
  • detect possibly equivalent nodes using simulation
  • candidate constant nodes
  • candidate equivalent nodes
  • run SAT on the intermediate miters in a
    topological order
  • refine candidates using counterexamples

Proving internal equivalences in a topological
Improved CEC (command cec)
  • For hard CEC instances
  • Heuristic skip some equivalences
  • Results in
  • 5x reduction in runtime
  • Solving previously unresolved problems
  • Given a combinational miter with equivalence
    class A, B, A, B
  • Possible equivalences
  • A B, A A, A B, B A, B B, A B
  • only try to prove AA and BB
  • do not try to prove
  • A B, A B, A B A B

CEC Under Permutation
Yes or No (and counterexample)
Yes or No (and counterexample)
Boolean matcher
  • A resource-aware combination of graph-based,
    simulation-based, and SAT-based techniques
  • Works for circuits with 100s of I/Os in about 1
  • ABC command bm (developed at U of Michigan)
  • Hadi Katebi and Igor Markov, Large-scale Boolean
    Matching, Proc. DATE10.

HWMCC 2011
  • 4th Hardware Model Checking Competition
  • Held at FMCAD11 in Austin, TX (Oct 30 Nov 2,
  • Organized by
  • Armin Biere, Keijo Heljanko, Siert Wieringa,
    Niklas Soerensson
  • Participants
  • 6 universities submitted 14 solvers 4 solvers
    that won previous competitions
  • Benchmarks
  • 465 benchmarks from different sources
  • Resources
  • 15 min, 7Gb RAM, 4 cores
  • Using 32 node cluster, Intel Quad Core 2.6 GHz, 8
    GB, Ubuntu

Courtesy Armin Biere
Courtesy Armin Biere
Courtesy Armin Biere
Future Work
  • Exploring new directions
  • Satisfiability Modulo Theories (SMT)
  • Software verification
  • Using concurrency, etc
  • Improving bit-level engines
  • Application-specific SAT solvers
  • A modern BDD package
  • Improved sequential logic simulators
  • combining random, guided and symbolic simulation
  • Improved abstraction refinement
  • and may be a new engine or two

To Learn More
  • Visit BVSRC webpage
  • Read recent papers http//
  • Send email

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