Theoretical Computer Science
Journal of the ACM (JACM)
Minimization algorithms for sequential transducers
Theoretical Computer Science
Multiobjective query optimization
PODS '01 Proceedings of the twentieth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Introduction to Automata Theory, Languages, and Computation (3rd Edition)
Introduction to Automata Theory, Languages, and Computation (3rd Edition)
Lower bounds for natural proof systems
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
CSL '08 Proceedings of the 22nd international workshop on Computer Science Logic
LICS '11 Proceedings of the 2011 IEEE 26th Annual Symposium on Logic in Computer Science
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
Quantitative reactive modeling and verification
Computer Science - Research and Development
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Additive Cost Register Automata (ACRA) map strings to integers using a finite set of registers that are updated using assignments of the form "x:=y+c" at every step. The corresponding class of additive regular functions has multiple equivalent characterizations, appealing closure properties, and a decidable equivalence problem. In this paper, we solve two decision problems for this model. First, we define the register complexity of an additive regular function to be the minimum number of registers that an ACRA needs to compute it. We characterize the register complexity by a necessary and sufficient condition regarding the largest subset of registers whose values can be made far apart from one another. We then use this condition to design a pspace algorithm to compute the register complexity of a given ACRA, and establish a matching lower bound. Our results also lead to a machine-independent characterization of the register complexity of additive regular functions. Second, we consider two-player games over ACRAs, where the objective of one of the players is to reach a target set while minimizing the cost. We show the corresponding decision problem to be exptime-complete when the costs are non-negative integers, but undecidable when the costs are integers.