Design from semantics first
Identify the objects and values that are meaningful in the application: characters, tokens, states, measurements, commands, classes, or identifiers.
Semantics-Driven Hardware Design
Digital hardware begins with meaning—not with every possible bit pattern.
Many applications use only a restricted subset of the values their binary encodings can represent. Those semantic restrictions naturally induce Partially Defined Boolean Functions.
Encoding Domain
012…63
↓ application semantics
Semantic Domain
012…32
Only meaningful values constrain the implementation. The remaining encodings create native optimization freedom.
01
The starting point
Understand what the hardware actually processes
Traditional synthesis begins with a Boolean function over the complete encoding domain. Semantics-driven design begins one step earlier by identifying the application’s meaningful data domain.
A
Characters
A 6-bit code represents 64 values, but an application may support only 33 characters.
B
Calendar values
Four bits represent 16 values, while a month field admits only values 1 through 12.
C
AI vocabulary IDs
An identifier bus may encode far more values than the model’s trained vocabulary contains.
D
Medical measurements
Sensor encodings may include combinations outside the physical or clinically meaningful range.
E
Protocol symbols
Reserved message types, illegal opcodes, and forbidden command combinations are outside the semantic domain.
F
Sequential behavior
Unreachable states and state/input combinations are native unspecified behavior.
02
Native partial definition
Semantic restrictions naturally create PDBFs
Binary encoding spaceAll representable bit patterns
−
Semantic domainValues meaningful to the application
=
Native unspecified regionOptimization freedom for GT
Native PDBF principle. When the application’s semantic domain occupies only a subset of the available encoding space, behavior outside that domain need not constrain the implementation.
GT does not invent these don’t-care conditions. They already exist because the application never requires meaningful behavior for invalid or impossible values. GT exposes the corresponding Opportunity Space and searches for a favorable Legal Completion.
03
The design method
Three steps from meaning to optimized hardware
Synthesize from PDBFs second
Specify behavior only for the valid semantic domain. Leave invalid, impossible, or unsupported encodings outside the required function.
Optimize with GT third
Search the Opportunity Space to find a Legal Completion that improves gate count, logic depth, wiring, fan-out, power, or another objective.
Design from semantics first.
Synthesize from PDBFs second.
Optimize with GT third.
04
Measured example
Three-way comparison of restricted 6-bit character codes
Two characters are represented by 6-bit values, but only codes 0 through 32 are used. The comparator produces three one-hot outputs:
| Relation | LT EQ GT |
|---|---|
| A < B | 100 |
| A = B | 010 |
| A > B | 001 |
Of 4,096 possible input pairs, only 1,089 belong to the semantic domain. The other 3,007 combinations remain unspecified.
Specified semantic domain1,089
Native unspecified region3,007
73.4% of the encoding space becomes native optimization freedom.
| Method / Objective | Gates | Maximum levels | Wires |
|---|---|---|---|
| ABC + deepsyn | 41 | 9 | 85 |
| GT — minimum gates | 29 | 9 | 61 |
| GT — minimum depth | 37 | 8 | 77 |
29.3%gate reduction at equal depth
28.2%wire reduction at equal depth
11.1%depth reduction with fewer gates
The comparator demonstrates the central idea: conventional synthesis optimizes a function over a completed encoding domain, while GT searches completions that preserve only the application’s valid semantic behavior.
05
Where native PDBFs arise
A broad design opportunity
| Application domain | Source of native partial definition |
|---|---|
| Character and text processing | Unsupported or illegal character codes |
| AI token processing | Identifiers outside the model vocabulary |
| Classification hardware | Unused labels and impossible feature combinations |
| Calendar and time logic | Invalid months, days, hours, or dates |
| Medical and environmental sensing | Values outside the physical operating range |
| Robotics and targeting | Impossible distances, modes, and sensor combinations |
| Network and communication protocols | Reserved symbols and forbidden message sequences |
| RTL datapaths | Contextually unreachable local terms |
| Sequential controllers | Unreachable states and state/input combinations |
This page presents a design philosophy and a growing research direction. The GT Synthesis trilogy establishes how PDBFs can be optimized and how they arise from context and reachability. Semantics-driven hardware design asks a broader engineering question: which encoded values are actually meaningful?
Traditional synthesis begins with bits.
GT Synthesis begins with meaning.
Whenever semantics restrict the encoding domain, a Native PDBF may already be present.
Explore GT Theory