Decidable Models of Recursive Asynchronous Concurrency

Asynchronously communicating pushdown systems (ACPS) that satisfy the empty-stack constraint (a pushdown process may receive only when its stack is empty) are a popular decidable model for recursive programs with asynchronous atomic procedure calls. We study a relaxation of the empty-stack constraint for ACPS that permits concurrency and communication actions at any stack height, called the shaped stack constraint, thus enabling a larger class of concurrent programs to be modelled. We establish a close connection between ACPS with shaped stacks and a novel extension of Petri nets: Nets with Nested Coloured Tokens (NNCTs). Tokens in NNCTs are of two types: simple and complex. Complex tokens carry an arbitrary number of coloured tokens. The rules of NNCT can synchronise complex and simple tokens, inject coloured tokens into a complex token, and eject all tokens of a specified set of colours to predefined places. We show that the coverability problem for NNCTs is Tower-complete. To our knowledge, NNCT is the first extension of Petri nets, in the class of nets with an infinite set of token types, that has primitive recursive coverability. This result implies Tower-completeness of coverability for ACPS with shaped stacks

Bayesian Inference of Social Norms as Shared Constraints on Behavior

People act upon their desires, but often, also act in adherence to implicit social norms. How do people infer these unstated social norms from others' behavior, especially in novel social contexts? We propose that laypeople have intuitive theories of social norms as behavioral constraints shared across different agents in the same social context. We formalize inference of norms using a Bayesian Theory of Mind approach, and show that this computational approach provides excellent predictions of how people infer norms in two scenarios. Our results suggest that people separate the influence of norms and individual desires on others' actions, and have implications for modelling generalizations of hidden causes of behavior.Comment: 7 pages, 5 figures, to appear in CogSci 2019, code available at https://github.com/ztangent/norms-cogsci1