Pushdown automaton

About: Pushdown automaton is a research topic. Over the lifetime, 1868 publications have been published within this topic receiving 35399 citations.

Memory-Augmented Recurrent Neural Networks Can Learn Generalized Dyck Languages

Abstract: We introduce three memory-augmented Recurrent Neural Networks (MARNNs) and explore their capabilities on a series of simple language modeling tasks whose solutions require stack-based mechanisms. We provide the first demonstration of neural networks recognizing the generalized Dyck languages, which express the core of what it means to be a language with hierarchical structure. Our memory-augmented architectures are easy to train in an end-to-end fashion and can learn the Dyck languages over as many as six parenthesis-pairs, in addition to two deterministic palindrome languages and the string-reversal transduction task, by emulating pushdown automata. Our experiments highlight the increased modeling capacity of memory-augmented models over simple RNNs, while inflecting our understanding of the limitations of these models.

On the complexity of checking semantic equivalences between pushdown processes and finite-state processes

Abstract: Simulation preorder/equivalence and bisimulation equivalence are the most commonly used equivalences in concurrency theory. Their standard definitions are often called strong simulation/bisimulation, while weak simulation/bisimulation abstracts from internal @t-actions. We study the computational complexity of checking these strong and weak semantic preorders/equivalences between pushdown processes and finite-state processes. We present a complete picture of the computational complexity of these problems and also study fixed-parameter tractability in two important input parameters: x, the size of the finite control of the pushdown process, and y, the size of the finite-state process. All simulation problems are generally EXPTIME-complete and only become polynomial if both parameters x and y are fixed. Weak bisimulation equivalence is PSPACE-complete, but becomes polynomial if and only if parameter x is fixed. Strong bisimulation equivalence is PSPACE-complete, but becomes polynomial if either parameter x or y is fixed.

A context-free language which is not acceptable by a probabilistic automaton

Abstract: A linear context-free language which is not acceptable by a finite probabilistic automaton is given, and it is shown that the family of stochastic languages is not closed under concatenation and homomorphism.

Query Automata for Nested Words

Abstract: We study visibly pushdown automata (VPA) models for expressing and evaluating queries on words with a nesting structure. We define a query VPA model, which is a 2-way deterministic VPA that can mark in one run all positions in a document that satisfy a query, and show that it is equi-expressive as unary monadic queries. This surprising result parallels a classic result by Hopcroft and Ullman for queries on regular word languages. We also compare our model to query models on unranked trees, and show that our result is fundamentally different from those known for automata on trees.