Matthew Hague Royal Holloway, University of London
An incomplete list of contributors:
Taolue Chen (University of Surrey) Riccardo De Masellis (Uppsala University) Alejandro Flores-Lamas, Matthew Hague (Royal Holloway, University of London) Zhilei Han (Tsinghua University) Denghang Hu (University of Chinese Academy of Sciences) Anthony W. Lin, Oliver Markgraf (TU Kaiserslautern) Philipp Rümmer (University of Regensburg) Zhilin Wu (State Key Laboratory of Computer Science)
Publications: POPL 2016, POPL 2018, POPL 2019, ATVA 2020, POPL 2022
SMTCOMP 2022: Best complementary solver for UNSAT instances SMTCOMP 2023: Best overall in QF_S category
For a simple word equation
Rewrite into "solved form"
Now solve the solved form
Propagate to :
Propagate to via :
Contradiction
OSTRICH uses proof rules to search for a solution or contradiction.
We write rules upwards
From we can add .
"Standard" rules. E.g.
Notice branches, both branches need to be closed.
The more interesting rules propagate regular constraints
Is this enough to solve
No: what do we do with ?
is really a string function
Or more precisely
For concat, we can have a rule
is still regular
Given
We can push forwards through to get
On the condition that is still regular
Works for multiple arguments
We can support several string functions with forward propagation
What about and ?
( )
Replace each instance of "cat" in with "leopard"
For fixed strings is still regular.
What if the leopard is a variable?
Non-regular
We can't combine these to get a regular constraint on
because is not regular.
We can combine
to get a regular constraint on .
That is, is regular.
What about
We have the following constraints on and .
We don't get separate constraints on and :
Allows e.g. and .
A recognisable constraint is a finite-union of regular products.
In general
In general, for we require
We then get the backwards rule
Several functions can run backwards, even if they are not forward-able.
Capture groups handled used prioritised streaming string transducers.
Complexity ranges from polynomial to a tower of exponentials.
Forward propagation tends to be cheaper, backwards richer.
We can conclude UNSAT if we find contradictory constraints
When can we conclude SAT?
A straight-line string constraint is of the form
where is only used after its "definition" .
Can be generalised to "chain-free".
(For non-straight-line constraints, we also have other ways of using SAT that can assign values using a rule and eliminate function applications to leave only regular constraints.)
OSTRICH currently has limited support for integer functions.
However, OSTRICH-CEA uses cost-enriched finite automata to model string/integer functions.
Future work