Departmental Papers (CIS)
Document Type
Conference Paper
Date of this Version
2-23-2012
Abstract
Motivated by the successful application of the theory of regular languages to formal verification of finite-state systems, there is a renewed interest in developing a theory of analyzable functions from strings to numerical values that can provide a foundation for analyzing quantitative properties of finite-state systems. In this paper, we propose a deterministic model for associating costs with strings that is parameterized by operations of interest (such as addition, scaling, and min), a notion of regularity that provides a yardstick to measure expressiveness, and study decision problems and theoretical properties of resulting classes of cost functions. Our definition of regularity relies on the theory of string-to-tree transducers, and allows associating costs with events that are conditional upon regular properties of future events. Our model of cost register automata allows computation of regular functions using multiple "write-only" registers whose values can be combined using the allowed set of operations. We show that classical shortest-path algorithms as well as algorithms designed for computing discounted costs, can be adopted for solving the min-cost problems for the more general classes of functions specified in our model. Cost register automata with min and increment give a deterministic model that is equivalent to weighted automata, an extensively studied nondeterministic model, and this connection results in new insights and new open problems.
Date Posted: 18 July 2012
Comments
ALur, R., D'Antoni, L., Deshmukh, J., Raghothaman, M., & Yuan, Y., Regular Functions, Cost Register Automata, and Generalized Min-Cost Problems, CoRR, 2012, http://arxiv.org/abs/1111.0670