Nuclear arms control: optimising verification processes through formal modelling
Technical paper presented at the 2016 Defence and Security Doctoral Symposium.
Arms control verification processes do not in practice allow for the parties involved to gather complete information about each other. Instead, each must make decisions about whether or not other parties are complying with their obligations on the basis of limited information. They must also make decisions during negotiation of a verification regime about the measures to be used, and during implementation of that regime about how and when to use the tools at their disposal. Decision-making under uncertainty is therefore a core element of the arms control verification problem. Our work aims to extend and combine mathematical modelling and verification approaches such that they can cope with the inherent lack of available data in this domain, and potentially be used to support policy-makers in practice.
Our approach is to model the beliefs of each party and the various inspection control processes in a type of software known as a Satisfiability Modulo Theories (SMT) solver. This offers a general purpose approach to the automated analysis of mathematical models; in our case we use SMT to deal with uncertainty in (or absence of) data by expressing them as under-specifications of parameters in model verification processes. In other words, we don’t have to choose values for parameters – such as the number of nuclear weapons that one of the parties holds, for example – if we don’t know them: we can pick a range of possible values, or leave the value totally unconstrained.
We demonstrate the capabilities of this approach by exploring a representative, quantitative model of an arms control process in which two parties engage in mutual nuclear arms reduction and verification activities. We show that we are able to answer pertinent questions such as “given uncertainty in our treaty partners’ initial weapon stockpile, with scheduled inspections every 6 months and 2 other unscheduled inspections per year, what timing for unscheduled inspections leads to the minimum difference between our partners’ declaration and our assessment of their actual arsenal?”
These new modelling and analysis methods allow for a much more sophisticated approach to modelling arms control: we have harnessed a supercomputer to analyse over 134 million possible inspection timelines, allowing the software to compute an inspection schedule over a treaty lifespan of 2 years for which performance against one or more measures of interest is optimised. The models and results can then be studied and their expected outcomes assessed to assist in decision-making regarding proposed arms control regimes.
Paul Beaumont is a final year Postgraduate Research student in the Department of Computing at Imperial College London. His PhD focusses on understanding and solving mathematical models in the absence of data, and follows on from a Masters and undergraduate in Mathematics, also at Imperial. He works with colleagues from AWE and is applying his PhD techniques to the problem of nuclear arms verification.