A decidable policy language for history-based transaction monitoring

TL;DR

This paper introduces a decidable, expressive policy language based on extended linear temporal logic for monitoring transaction histories, enabling trust assessment in online trading with proven computational complexity bounds.

Contribution

It develops an extended linear temporal logic for specifying transaction policies, proves the decidability and complexity of model checking, and addresses partial observability scenarios.

Findings

Model checking is PSPACE-complete in general.

Decidability is achieved for fixed policies.

Partial observability monitoring is decidable under restrictions.

Abstract

Online trading invariably involves dealings between strangers, so it is important for one party to be able to judge objectively the trustworthiness of the other. In such a setting, the decision to trust a user may sensibly be based on that user's past behaviour. We introduce a specification language based on linear temporal logic for expressing a policy for categorising the behaviour patterns of a user depending on its transaction history. We also present an algorithm for checking whether the transaction history obeys the stated policy. To be useful in a real setting, such a language should allow one to express realistic policies which may involve parameter quantification and quantitative or statistical patterns. We introduce several extensions of linear temporal logic to cater for such needs: a restricted form of universal and existential quantification; arbitrary computable functions and relations in the term language; and a "counting" quantifier for counting how many times a formula holds in the past. We then show that model checking a transaction history against a policy, which we call the history-based transaction monitoring problem, is PSPACE-complete in the size of the policy formula and the length of the history. The problem becomes decidable in polynomial time when the policies are fixed. We also consider the problem of transaction monitoring in the case where not all the parameters of actions are observable. We formulate two such "partial observability" monitoring problems, and show their decidability under certain restrictions.