# Semantic expressive capacity with bounded memory

## TL;DR

This paper explores the limits of semantic parsing mechanisms, showing that projective systems require unbounded memory to represent certain relations, unlike nonprojective systems, impacting both grammar-based and neural models.

## Contribution

It provides the first proof demonstrating the memory requirements for projective semantic parsing mechanisms, highlighting fundamental differences from nonprojective systems.

## Key findings

- Projective mechanisms need unbounded memory for certain relations
- Nonprojective mechanisms can represent these relations without unbounded memory
- Implications for the design of grammar-based and neural semantic parsers

## Abstract

We investigate the capacity of mechanisms for compositional semantic parsing to describe relations between sentences and semantic representations. We prove that in order to represent certain relations, mechanisms which are syntactically projective must be able to remember an unbounded number of locations in the semantic representations, where nonprojective mechanisms need not. This is the first result of this kind, and has consequences both for grammar-based and for neural systems.