Light-weight Antimirov cofactors for seq_monadic
================================================
Overview
--------
The seq_monadic solver explores symbolic regex derivatives when
computing live
states and product transitions. Its original transition representation
used
Brzozowski cofactors.
This change adds a light-weight Antimirov representation. It first
computes the
existing Brzozowski cofactors and then decomposes targets whose outer
shape is
s1 | ... | sn
or
(s1 | ... | sn) . tail
into separate transitions. Concatenations are maintained in
right-associative
form, so a distributable union occurs as the head of the concatenation.
Targets are reconstructed with mk_regex_concat to preserve
normalization.
After decomposition, transitions with the same target are merged by
disjoining
their guards. The existing path-aware cofactor traversal and range
predicates
are therefore retained.
Example
-------
For
r = .* a .{k}
the Brzozowski cofactors have the shape
[a, r | .{k}]
[^a, r]
The light-weight Antimirov transformation produces
[., r]
[a, .{k}]
This preserves the language while avoiding the deterministic subset
states
that grow exponentially on this family.
Modes
-----
seq_monadic exposes two transition modes:
light_antimirov default
brzozowski retained as an explicit option
The implementation is seq_rewriter::light_ant_derivative_cofactors.
Correctness
-----------
The seq_monadic unit tests run in both modes. They cover character and
generic
element sequences, multiple and repeated variables, variable
constraints,
bounded loops, conjunctions of memberships, and witness construction. A
focused test checks the cofactor transformation above. The complete
94-test
unit suite used during evaluation passed. The benchmark harness is not
registered as a normal unit test; after detaching it, all 93 registered
tests
pass.
Benchmark evaluation
--------------------
The final optimized comparison used all 1,545 SMT2 files under
C:\git\bench\inputs\regexes. Each file was run in a separate process
with a
15-second timeout. There were 1,513 cases where both modes completed
without a
process failure or timeout.
Brzozowski Light-Ant
paired solver time 94.98 s 63.26 s
median solver time 1.734 ms 0.710 ms
derivative calls 5.70 M 3.39 M
cofactors 13.33 M 6.99 M
live states 2.74 M 0.44 M
product states 652.8 K 642.8 K
Light-Ant reduced paired solver time by 33.4%, derivative calls by
40.5%,
cofactors by 47.5%, and live states by 84.0%. It was faster on 1,091
cases;
Brzozowski was faster on 421 cases.
Light-Ant changed 131 Brzozowski undef results to sat. There were no
reverse
verdict changes and no mismatches against known sat/unsat statuses. Both
modes
had two timeouts. Process failures decreased from 30 to 27.
By corpus, paired solver time improved by 39.1% on ClemensRegex and by
11.9% on
MargusRegex.
Alternatives considered
-----------------------
Direct use of full Antimirov derivatives was also evaluated. It
introduced
large performance outliers, particularly around intersections, and
produced
additional undef results and timeouts. Disabling intersection-over-union
distribution improved some of these cases but remained slower and less
robust
than the light-weight transformation. The direct full-Ant mode was
therefore
removed from this change.
Copilot-Session: a2ce3573-4e15-4a4a-afb5-21e3cb04e4a2
|
||
|---|---|---|
| .github | ||
| a3 | ||
| cmake | ||
| codeql/custom_queries | ||
| contrib | ||
| doc | ||
| docker | ||
| examples | ||
| noarch | ||
| resources | ||
| scripts | ||
| src | ||
| .bazelrc | ||
| .clang-format | ||
| .dockerignore | ||
| .gitattributes | ||
| .gitignore | ||
| BUILD.bazel | ||
| build_z3.bat | ||
| CMakeLists.txt | ||
| configure | ||
| LICENSE.txt | ||
| MODULE.bazel | ||
| README-CMake.md | ||
| README.md | ||
| RELEASE_NOTES.md | ||
| Z3-AGENT.md | ||
| z3.log | ||
| z3.pc.cmake.in | ||
| z3guide.jpeg | ||
Z3
Z3 is a theorem prover from Microsoft Research. It is licensed under the MIT license. Windows binary distributions include C++ runtime redistributables
If you are not familiar with Z3, you can start here.
Pre-built binaries for stable and nightly releases are available here.
Z3 can be built using Visual Studio, a Makefile, using CMake, using vcpkg, or using Bazel. It provides bindings for several programming languages.
See the release notes for notes on various stable releases of Z3.
Build status
Pull Request & Push Workflows
| WASM Build | Windows Build | CI | OCaml Binding |
|---|---|---|---|
Scheduled Workflows
| Open Bugs | Android Build | Pyodide Wheel (PyPI) | Nightly Build | Cross Build | F* Master Build |
|---|---|---|---|---|---|
| MSVC Static | MSVC Clang-CL | Build Z3 Cache | Memory Safety | Mark PRs Ready |
|---|---|---|---|---|
Manual & Release Workflows
| Documentation | Release Build | WASM Release |
|---|---|---|
Specialized Workflows
| Nightly Validation | Copilot Setup | Agentics Maintenance |
|---|---|---|
Agentic Workflows
| API Coherence | Code Simplifier | Release Notes | Workflow Suggestion | Academic Citation |
|---|---|---|---|---|
| Issue Backlog | Memory Safety Report | Specbot Crash Analyzer | SMTLIB Benchmark Finder |
|---|---|---|---|
| TPTP Benchmark |
|---|
Building Z3 on Windows using Visual Studio Command Prompt
For 32-bit builds, start with:
python scripts/mk_make.py
or instead, for a 64-bit build:
python scripts/mk_make.py -x
then run:
cd build
nmake
Z3 uses C++20. The recommended version of Visual Studio is therefore VS2019 or later.
Security Features (MSVC): When building with Visual Studio/MSVC, a couple of security features are enabled by default for Z3:
- Control Flow Guard (
/guard:cf) - enabled by default to detect attempts to compromise your code by preventing calls to locations other than function entry points, making it more difficult for attackers to execute arbitrary code through control flow redirection - Address Space Layout Randomization (
/DYNAMICBASE) - enabled by default for memory layout randomization, required by the/GUARD:CFlinker option - These can be disabled using
python scripts/mk_make.py --no-guardcf(Python build) orcmake -DZ3_ENABLE_CFG=OFF(CMake build) if needed
Building Z3 using make and GCC/Clang
Execute:
python scripts/mk_make.py
cd build
make
sudo make install
Note by default g++ is used as C++ compiler if it is available. If you
prefer to use Clang, change the mk_make.py invocation to:
CXX=clang++ CC=clang python scripts/mk_make.py
Note that Clang < 3.7 does not support OpenMP.
You can also build Z3 for Windows using Cygwin and the Mingw-w64 cross-compiler. In that case, make sure to use Cygwin's own Python and not some Windows installation of Python.
For a 64-bit build (from Cygwin64), configure Z3's sources with
CXX=x86_64-w64-mingw32-g++ CC=x86_64-w64-mingw32-gcc AR=x86_64-w64-mingw32-ar python scripts/mk_make.py
A 32-bit build should work similarly (but is untested); the same is true for 32/64 bit builds from within Cygwin32.
By default, it will install z3 executables at PREFIX/bin, libraries at
PREFIX/lib, and include files at PREFIX/include, where the PREFIX
installation prefix is inferred by the mk_make.py script. It is usually
/usr for most Linux distros, and /usr/local for FreeBSD and macOS. Use
the --prefix= command-line option to change the install prefix. For example:
python scripts/mk_make.py --prefix=/home/leo
cd build
make
make install
To uninstall Z3, use
sudo make uninstall
To clean Z3, you can delete the build directory and run the mk_make.py script again.
Building Z3 using CMake
Z3 has a build system using CMake. Read the README-CMake.md file for details. It is recommended for most build tasks, except for building OCaml bindings.
Building Z3 using vcpkg
vcpkg is a full platform package manager. To install Z3 with vcpkg, execute:
git clone https://github.com/microsoft/vcpkg.git
./bootstrap-vcpkg.bat # For powershell
./bootstrap-vcpkg.sh # For bash
./vcpkg install z3
Building Z3 using Bazel
Z3 can be built using Bazel. This is known to work on Ubuntu with Clang (but may work elsewhere with other compilers):
bazel build //...
Dependencies
Z3 itself has only few dependencies. It uses C++ runtime libraries, including pthreads for multi-threading. It is optionally possible to use GMP for multi-precision integers, but Z3 contains its own self-contained multi-precision functionality. Python is required to build Z3. Building Java, .NET, OCaml and Julia APIs requires installing relevant toolchains.
Z3 bindings
Z3 has bindings for various programming languages.
.NET
You can install a NuGet package for the latest release Z3 from nuget.org.
Use the --dotnet command line flag with mk_make.py to enable building these.
See examples/dotnet for examples.
C
These are always enabled.
See examples/c for examples.
C++
These are always enabled.
See examples/c++ for examples.
Java
Use the --java command line flag with mk_make.py to enable building these.
For IDE setup instructions (Eclipse, IntelliJ IDEA, Visual Studio Code) and troubleshooting, see the Java IDE Setup Guide.
See examples/java for examples.
Go
Use the --go command line flag with mk_make.py to enable building these. Note that Go bindings use CGO and require a Go toolchain (Go 1.20 or later) to build.
With CMake, use the -DZ3_BUILD_GO_BINDINGS=ON option.
See examples/go for examples and src/api/go/README.md for complete API documentation.
OCaml
Use the --ml command line flag with mk_make.py to enable building these.
See examples/ml for examples.
Python
You can install the Python wrapper for Z3 for the latest release from pypi using the command:
pip install z3-solver
Use the --python command line flag with mk_make.py to enable building these.
Note that it is required on certain platforms that the Python package directory
(site-packages on most distributions and dist-packages on Debian-based
distributions) live under the install prefix. If you use a non-standard prefix
you can use the --pypkgdir option to change the Python package directory
used for installation. For example:
python scripts/mk_make.py --prefix=/home/leo --python --pypkgdir=/home/leo/lib/python-2.7/site-packages
If you do need to install to a non-standard prefix, a better approach is to use
a Python virtual environment
and install Z3 there. Python packages also work for Python3.
Under Windows, recall to build inside the Visual C++ native command build environment.
Note that the build/python/z3 directory should be accessible from where Python is used with Z3
and it requires libz3.dll to be in the path.
virtualenv venv
source venv/bin/activate
python scripts/mk_make.py --python
cd build
make
make install
# You will find Z3 and the Python bindings installed in the virtual environment
venv/bin/z3 -h
...
python -c 'import z3; print(z3.get_version_string())'
...
See examples/python for examples.
Julia
The Julia package Z3.jl wraps the C API of Z3. A previous version of it wrapped the C++ API: Information about updating and building the Julia bindings can be found in src/api/julia.
WebAssembly / TypeScript / JavaScript
A WebAssembly build with associated TypeScript typings is published on npm as z3-solver. Information about building these bindings can be found in src/api/js.
Smalltalk (Pharo / Smalltalk/X)
Project MachineArithmetic provides a Smalltalk interface to Z3's C API. For more information, see MachineArithmetic/README.md.
AIX
Build settings for AIX are described here.
System Overview
Interfaces
-
Default input format is SMTLIB2
-
Other native foreign function interfaces:
-
Python API (also available in pydoc format)
-
C
-
OCaml
-
Smalltalk (supports Pharo and Smalltalk/X)
Power Tools
- The Axiom Profiler currently developed by ETH Zurich

