Z3, a state-of-the-art Satisfiability Modulo Theories (SMT) solver developed by Microsoft Research, supports a wide range of theories that are crucial for software verification and analysis. Here are some examples of the theories Z3 supports:
- Arithmetic: This includes both integer and real arithmetic, allowing Z3 to solve equations involving numbers.
- Fixed-size Bit-vectors: Useful for modeling digital circuits and binary data, these are vectors of bits with a fixed length.
- Extensional Arrays: Arrays are treated as functions from indices to values, enabling Z3 to reason about data structures.
- Datatypes: Z3 supports reasoning about complex data structures such as lists, trees, and records.
- Uninterpreted Functions: These are functions whose behavior is not defined, useful for abstracting away implementation details.
- Quantifiers: Z3 can handle both existential and universal quantifiers, allowing it to reason about properties that apply to all or some elements of a domain.
Additionally, Z3 can be extended or used in conjunction with other theories, such as Cardinality and Pseudo-Boolean inequalities, which are useful in combinatorial problems. It also supports encoding and axiomatizing custom theories, making it versatile for various applications in software verification and formal methods[3][4][9][10].
Citations:[1] https://theory.stanford.edu/~nikolaj/programmingz3.html
[2] https://specs.openstack.org/openstack/congress-specs/specs/rocky/alternative-engine-z3.html
[3] https://en.wikipedia.org/wiki/Z3_Theorem_Prover
[4] https://ceur-ws.org/Vol-418/paper10.pdf
[5] https://jfmc.github.io/z3-play/
[6] https://www21.in.tum.de/~boehmes/proofrec.pdf
[7] https://microsoft.github.io/z3guide/docs/logic/intro/
[8] https://stackoverflow.com/questions/73789804/theory-of-arrays-in-z3-1-model-is-difficult-to-understand-2-do-not-know-ho
[9] https://www.microsoft.com/en-us/research/wp-content/uploads/2016/02/nbjorner-aplas11.pdf
[10] https://theory.stanford.edu/~nikolaj/z3navigate.html