Document
Execution Trace Model
**Verifiable Semantic Execution Layer (VSEL)**
Verifiable Semantic Execution Layer (VSEL)
1. Purpose
This document defines the execution trace model of VSEL.
It specifies:
- how execution is recorded
- how traces are structured
- how traces map to formal semantics
- how traces are verified and reconstructed
The core requirement is:
Every semantically relevant state transition must be captured in a trace that is deterministic, complete, and verifiable.
2. Trace Definition
An execution trace is defined as:
[ \tau = (s_0, \sigma_0, s_1, \sigma_1, ..., \sigma_{n-1}, s_n) ]
Where:
- ( s_i \in S ) are states
- ( \sigma_i \in \Sigma ) are inputs
2.1 Trace Validity
A trace is valid if:
[ s_0 \in I \land \forall i: (s_i, \sigma_i, s_{i+1}) \in T ]
3. Concrete Trace Representation
A concrete trace ( \tau_c ) is composed of entries:
[ e_i = (id_i, s_i, \sigma_i, s_{i+1}, o_i, meta_i) ]
Where:
- ( id_i ): transition index
- ( s_i ): pre-state
- ( \sigma_i ): input
- ( s_{i+1} ): post-state
- ( o_i ): observable output
- ( meta_i ): auxiliary metadata
4. Trace Entry Structure
Each entry must satisfy:
4.1 Deterministic Indexing
[ id_i = i ]
Strict ordering enforced.
4.2 State Binding
[ Commit(s_i), Commit(s_{i+1}) ]
Must be included or derivable.
4.3 Input Binding
[ \sigma_i = Canonical(\sigma_i) ]
No ambiguity allowed.
4.4 Observable Binding
[ o_i = Obs(s_i, \sigma_i, s_{i+1}) ]
4.5 Metadata
Includes:
- timestamp
- execution domain
- sequence number
- previous commitment
Metadata must not influence semantics unless explicitly modeled.
5. Trace Commitment
The entire trace must be committed:
[ Commit(\tau) = Hash(Commit(e_0) | ... | Commit(e_n)) ]
Properties:
- tamper-evident
- order-preserving
- deterministic
6. Incremental Commitment Chain
Each entry links to the previous:
[ h_{i+1} = Hash(h_i | Commit(e_i)) ]
Ensures:
- sequential integrity
- no insertion/removal
7. Trace Completeness
A trace is complete if:
[ \forall \text{ state transitions}: \exists e_i ]
No hidden transitions allowed.
8. Trace Determinism
Given identical:
- initial state
- input sequence
- environment
The trace must be identical:
[ Replay(\tau) = \tau ]
9. Trace Canonicalization
All trace elements must be canonical:
- state encoding
- input encoding
- observable encoding
Equivalent semantics must yield identical trace representation.
10. Trace Reconstruction
Given:
- initial state ( s_0 )
- input sequence ( \sigma_0 ... \sigma_{n-1} )
The trace must be reconstructible:
[ Reconstruct(s_0, \sigma_0 ... \sigma_{n-1}) = \tau ]
11. Trace Verification
To verify a trace:
- verify initial state validity
- verify each transition
- verify invariant preservation
- verify commitment chain
- verify observables
[ ValidTrace(\tau) ]
12. Partial Trace Verification
Supports:
- segment verification
- inclusion proofs
Using:
- Merkle structures
- commitment proofs
13. Trace Compression
Trace may be compressed:
[ \tau_{compressed} = Compress(\tau) ]
Constraints:
- must preserve semantics
- must be reversible or provable
14. Trace and Proof Relationship
Proofs operate over traces:
[ \pi = Proof(\tau) ]
Trace must be:
- fully represented in witness
- bound to commitments
15. Cross-Layer Mapping
15.1 Trace ↔ Semantic Mapping
[ \mu_{Tr}(\tau_c) = \tau_f ]
15.2 Trace ↔ Constraints
[ \tau \Rightarrow SatisfiesConstraints(\tau) ]
15.3 Trace ↔ Proof
[ Verify(\pi) \Rightarrow ValidTrace(\tau) ]
16. Trace Ordering Guarantees
Trace ordering must satisfy:
[ i < j \Rightarrow Order(e_i, e_j) ]
Unless explicitly relaxed by model.
17. Temporal Consistency
Trace must preserve:
- monotonic time
- sequence consistency
[ meta_{i+1}.time \geq meta_i.time ]
18. Failure Modes
18.1 Missing Transitions
State changes not recorded.
18.2 Out-of-Order Entries
Incorrect ordering.
18.3 Inconsistent State Linking
[ s_{i+1} \neq s'_{i+1} ]
18.4 Observable Mismatch
[ o_i \neq Obs(s_i, \sigma_i, s_{i+1}) ]
18.5 Non-Deterministic Replay
Trace cannot be reproduced.
18.6 Commitment Break
Hash chain invalid.
19. Minimal Trace Validity Conditions
A valid trace must satisfy:
- completeness
- determinism
- correct ordering
- invariant preservation
- valid commitments
20. Closing Statement
The trace is the ground truth of execution.
Proofs attest to it. Specifications define it. But the trace is what actually happened.
If the trace is incomplete or ambiguous, the system is unverifiable, no matter how strong the proof system is.