Automata on Infinite Objects and Church's Problem
Automata on Infinite Objects and Church's Problem
Cosmological lower bound on the circuit complexity of a small problem in logic
Journal of the ACM (JACM)
CIAA '00 Revised Papers from the 5th International Conference on Implementation and Application of Automata
Optimizations for LTL Synthesis
FMCAD '06 Proceedings of the Formal Methods in Computer Aided Design
From program verification to program synthesis
Proceedings of the 37th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Verification of data paths using unbounded integers: automata strike back
HVC'06 Proceedings of the 2nd international Haifa verification conference on Hardware and software, verification and testing
PLDI '10 Proceedings of the 2010 ACM SIGPLAN conference on Programming language design and implementation
Synthesis for regular specifications over unbounded domains
Proceedings of the 2010 Conference on Formal Methods in Computer-Aided Design
Synthesis of Reactive(1) designs
Journal of Computer and System Sciences
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We propose to describe computations using QFPAbit, a language of quantifier-free linear arithmetic on unbounded integers with bitvector operations. We describe an algorithm that, given a QFPAbit formula with input and output variables denoting integers, generates an efficient function from a sequence of inputs to a sequence of outputs, whenever such function on integers exists. The starting point for our method is a polynomial-time translation mapping a QFPAbit formula into the sequential circuit that checks the correctness of the input/output relation. From such a circuit, our synthesis algorithm produces solved circuits from inputs to outputs that are no more than singly exponential in size of the original formula. In addition to the general synthesis algorithm, we present techniques that ensure that, for example, multiplication and division with large constants do not lead to an exponential blowup, addressing a practical problem with a previous approach that used the MONA tool to generate the specification automata.