Interchangeable Token Embeddings for Extendable Vocabulary and Alpha-Equivalence

We propose a novel approach for learning interchangeable tokens in language models to obtain an extendable vocabulary that can generalize to new tokens. Our method is designed to address alpha-equivalence, the principle that renaming bound variables in a syntactic expression preserves semantics. This property arises in many formal languages such as temporal logics, in which all proposition symbols represent the same concept but are distinguishable from each other. To handle such tokens, we develop a dual-part embedding approach. The first part is shared across all interchangeable tokens, thereby enforcing that they represent the same core concept. The second part is randomly generated for each token, which enables distinguishability. We evaluate our method in a Transformer encoder-decoder model on two tasks: solving linear temporal logic formulae and copying with extendable vocabulary. Our method demonstrates promising generalization capabilities in addition to introducing a favorable inductive bias for alpha-equivalence.

Learning to Estimate System Specifications in Linear Temporal Logic using Transformers and Mamba

Temporal logic is a framework for representing and reasoning about propositions that evolve over time. It is commonly used for specifying requirements in various domains, including hardware and software systems, as well as robotics. Specification mining or formula generation involves extracting temporal logic formulae from system traces and has numerous applications, such as detecting bugs and improving interpretability. Although there has been a surge of deep learning-based methods for temporal logic satisfiability checking in recent years, the specification mining literature has been lagging behind in adopting deep learning methods despite their many advantages, such as scalability. In this paper, we introduce autoregressive models that can generate linear temporal logic formulae from traces, towards addressing the specification mining problem. We propose multiple architectures for this task: transformer encoder-decoder, decoder-only transformer, and Mamba, which is an emerging alternative to transformer models. Additionally, we devise a metric for quantifying the distinctiveness of the generated formulae and a straightforward algorithm to enforce the syntax constraints. Our experiments show that the proposed architectures yield promising results, generating correct and distinct formulae at a fraction of the compute cost needed for the combinatorial baseline.

A Formal Methods Approach to Pattern Synthesis in Reaction Diffusion Systems

We propose a technique to detect and generate patterns in a network of locally interacting dynamical systems. Central to our approach is a novel spatial superposition logic, whose semantics is defined over the quad-tree of a partitioned image. We show that formulas in this logic can be efficiently learned from positive and negative examples of several types of patterns. We also demonstrate that pattern detection, which is implemented as a model checking algorithm, performs very well for test data sets different from the learning sets. We define a quantitative semantics for the logic and integrate the model checking algorithm with particle swarm optimization in a computational framework for synthesis of parameters leading to desired patterns in reaction-diffusion systems.