Memory Allocation

Boost.Parser seldom allocates memory. The exceptions to this are:

symbols allocates memory for the symbol/attribute pairs it contains. If symbols are added during the parse, allocations must also occur then. The data structure used by symbols is also a trie, which is a node-based tree. So, lots of allocations are likely if you use symbols.
The error handlers that can take a file name allocate memory for the file name, if one is provided.
If trace is turned on by passing boost::parser::trace::on to a top-level parsing function, the names of parsers are allocated.
When a failed expectation is encountered (using operator>), the name of the failed parser is placed into a std::string, which will usually cause an allocation.
string()'s attribute is a std::string, the use of which implies allocation. You can avoid this allocation by explicitly using a different string type for the attribute that does not allocate.
The attribute for repeat(p) in all its forms, including operator*, operator+, and operator%, is std::vector<ATTR(p)>, the use of which implies allocation. You can avoid this allocation by explicitly using a different sequence container for the attribute that does not allocate. boost::container::static_vector or C++26's std::inplace_vector may be useful as such replacements.

With the exception of allocating the name of the parser that was expected in a failed expectation situation, Boost.Parser does not does not allocate unless you tell it to, by using symbols, using a particular error_handler, turning on trace, or parsing into attributes that allocate.