Download presentation

Presentation is loading. Please wait.

Published byBrooke Reyes Modified over 4 years ago

1
1 Minimalist proof assistants Interactions of technology and methodology in formal system level verification Ken McMillan Cadence Berkeley Labs

2
2 Automated methods curve system size (bits of state) verification probability research systems 110100 10 3 10 4 10 5 10 6 10 7 100%

3
3 Automated methods curve system size (bits of state) verification probability unit-level FV decomposition 110100 10 3 10 4 10 5 10 6 10 7 100% bug finding verification

4
4 Proof assistants l General purpose proof assistants +Expressive logics +Integration with model checking l Problem: Do not naturally produce finite-state subgoals –Result: Detailed manual case analysis Complex global invariants Long, fragile proof scripts

5
5 What's missing... l Proof strategy that produces finite-state lemmas l Infrastructure to support this strategy l Reduced interactivity –more reusable proofs –no global invariants (too design-specific)

6
6 Minimalist proof assistant l Approach –Minimal logical expressiveness –Appropriate domain-specific proof strategy –Proof rules designed to support this strategy –All proof obligations reduced to model checking l Result –Short proofs –Proof goals reduced to tractable MC problems –Proofs more easily reused related: Seger 98

7
7 Rules built into SMV system... l Circular compositional rule –decomposition by refinement relations –auxiliary state l Temporal case analysis –path splitting l Symmetry reductions –reduce by symmetry to tractable number of cases l Data type reductions –large and infinite types –uninterpreted functions support general proof strategy...

8
8 Compositional refinement verification Abstract model System Translations

9
9 Localized verification Abstract model System Translations assumeprove

10
10 Localized verification Abstract model System Translations assume prove

11
11 Circular inference rule SPEC (related: AL 95, AH 96) 1 up to t -1 implies 2 up to t 2 up to t -1 implies 1 up to t always 1 and 2

12
12 SPEC Auxiliary variables aux P PA Q Q * A is definitional * Q does not reference A (related: Owicki, Gries)

13
13 SPEC P PA Big structures and path splitting i

14
14 Temporal case splitting l Prove separately that p holds at all times when v = i. l Path splitting v record register index i

15
15 SPEC P PA Case explosion and symmetry i k

16
16 Exploiting symmetry l Symmetric types –Semantics invariant under permutations of type. –Enforced by type checking rules. l Symmetry reduction rule * i is of scalarset type * P references only constants 0..k-1 of type (related: Murphi)

17
17 Data type reductions l Problem: large data types yield state explosion l Solution: reduce large (or infinite) types where T\i represents all the values in T except i. l Abstract interpretation Note: use in conjunction with case splitting

18
18 Data types with large ranges l Words, addresses, sequence numbers, tags, etc... l Example: content addressable memory KEYVALUE = = = = = = = QUERY

19
19 Summary of proof strategy l Control logic –Structural decomposition (comp. rule) l Data path –Refinement maps (comp. rule + aux.) –Decompose large structures (path splitting) –Reduce large types (data type reduction) Case reduction (symmetry)

20
20 Illustration: Tomasulos algorithm l Execute instructions in data flow order OP,DST opraoprb OP,DST opraoprb OP,DST opraoprb EU OPS TAGGED RESULTS INSTRUCTIONS VAL/TAG REG FILE

21
21 Compositional rule l Decompose into two lemmas OP,DST opraoprb OP,DST opraoprb OP,DST opraoprb EU OPS TAGGED RESULTS INSTRUCTIONS VAL/TAG REG FILE Lemma 1: Correct operands Lemma 2: Correct results

22
22 Proving the operand lemma OP,DST opraoprb OP,DST opraoprb OP,DST opraoprb EU OPS INSTRUCTIONS REG FILE VAL/TAG TAGGED RESULTS Lemma 1: Correct operands Lemma 2: Correct results "cone of influence" eliminates

23
23 Auxiliary variables in Tomasulo l Used to store correct operands and results for each instruction EU RESULTS INSTRUCTIONS OP,DST opraoprb O1O2R if (~stallout & opin=ALU){ next(aux[st].opra) := opra; next(aux[st].oprb) := oprb; next(aux[st].res) := res; } SPEC

24
24 Lemmas in SMV l Operand correctness forall (k in TAG) layer lemma1 : if (rs[k].valid & rs[k].opra.valid) rs[k].opra.val := aux[k].opra; l Result correctness forall (i in TAG) layer lemma2[i] : if (rb.tag = i & rb.valid) rb.val := aux[i].res;

25
25 Path splitting in Tomasulo OP,DST opraoprb OP,DST opraoprb OP,DST opraoprb EU OPS INSTRUCTIONS REG FILE VAL/TAG TAGGED RESULTS "cone of influence" eliminates

26
26 SMV implementation l Split cases of operand correctness on –producer reservation station –holding register l SMV implementation subcase lemma1[i][j] of rs[k]//lemma1 for rs[k].opra.tag = i & aux[k].srca = j;

27
27 Case explosion problem l Number of cases in operand correctness property: TAGS REGS TAGS = O(n 3 ) l Symmetric data type declarations scalarset REG 0..31; scalarset TAG 0..31; l SMV verifies types used in symmetric way

28
28 Symmetry reduction in operands lemma OP,DST opraoprb OP,DST opraoprb OP,DST opraoprb EU OPS INSTRUCTIONS REG FILE VAL/TAG TAGGED RESULTS i j k l Reduces by symmetry to two cases: (i = 0, j = 0, k = 0) (i = 0, j = 0, k = 1)

29
29 Type reduction: infinite-state Tomasulo l Scalarsets with undefined range l Data type reduction TAG->{i,k}, REG ->{j} l Only include values we care about in reduced type l Reduces variable encodings to –1 bit per variable of type REG –2 bits per variable of type TAG (related: Kurshan)

30
30 OP,DST Uninterpreted functions l Verify Tomasulo for arbitrary EU function f(a,b). f(a,b) RESULTS INSTRUCTIONS SPEC OP,DST opraoprb opraoprb OP,DST opraoprb f(a,b) OPS INSTRUCTIONS REG FILE VAL/TAG TAGGED RESULTS f(a,b) (related: Burch, Dill, Jones, etc...)

31
31 Case splitting l Prove result correctness only for specific cases, e.g. opra = 0, oprb = 1, f[0][1] = 2 OP,DST 01 opraoprb OP,DST opraoprb f(a,b) OPS INSTRUCTIONS REG FILE VAL/TAG 2 3! = 6 cases verified (related: Hojati, Singhal, Bryant, Clarke)

32
32 Result l Verification problem reduced to tractable MC problems –Max 25 state bits –11 cases of lemmas to verify after symmetry –Verification time less than 4 seconds l Tomasulo implementation proved for –Arbitrary number of registers, reservation stations –Arbitrary data word size and EU function l The proof is concise

33
33 Summary of approach l Auxiliary variables and circular rule –operand and result lemmas l Temporal case splitting –data path splitting l Symmetry reductions –reduce to tractable number of cases l Data type reductions –reduce large or infinite data types to small finite –uninterpreted functions for data operations

34
34 More examples l Applications of the same general strategy: –Infopad packet multiplexer –SGI cache coherence

35
35 InfoPad example (Truman 98) Bus Bridge ARM processor subsystem RX ASIC FPGA (FEC, timing,…) Video Pen Speech TX Audio/ Speech VGA control Wireless Modems 32-bit word 8-bit word Serial, FEC encoded Packet Buffer Memory

36
36 Packet streams Decomposition -- data integrity tag data Packet mux P P path splitting induction

37
37 Cache coherence (Eiriksson 98) S/F network protocol host protocol host protocol host Distributed cache coherence INTF PP MIO to net l Nondeterministic abstract model l Atomic actions l Single address abstraction l Verified coherence, etc...

38
38 Mapping protocol to RTL S/F network protocol host other hosts Abstract model CAM TABLES TAGS ~30K lines of verilog

39
39 Conclusions l Goal –System-level verification by model checking l Approach –Appropriate domain-specific proof strategy –Proof rules designed to support this strategy l Result –Proof goals reduced to tractable MC problems –Short proofs -- no global invariants

Similar presentations

OK

Basel-ICU-Journal Challenge18/20/2014. 2Basel-ICU-Journal Challenge8/20/2014.

Basel-ICU-Journal Challenge18/20/2014. 2Basel-ICU-Journal Challenge8/20/2014.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on australian continent vs usa Ppt on electricity billing system Ppt on credit default swaps and the financial crisis Ppt on display advertising Ppt on modern periodic table Ppt on computer languages of the 80's Ppt on blue eyes topic Ppt on digital media broadcasting projects Ppt on different occupations in nigeria Field emission display ppt online