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The known proofs that the equivalence and containment problems for the regular and for the linear context-free grammars are PSPACE-complete and undecidable, respecitvely, depend upon consideration of ambiguous grammars. We prove that this dependence is inherent. Deterministic polynomial time algorithms are presented for; (1) the equivalence and containment problems for the unambiguous regular grammars;...
Inductive inference machines (IIMs) are algorithmic devices which accept as input the graph of a computable function, an ordered pair at a time, and which output a succession of programs each conjectured to compute the input function. IIMs synthesize programs given examples of their intended input-output behavior. Several different criterion for successful synthesis by IIMs are defined. A given criterion...
We introduce a new complexity measure, QR[f(n)], which clocks the size of formulas from predicate calculus needed to express a given property. Techniques from logic are used to prove sharp lower bounds in the measure. These results demonstrate space requirements for computations and may provide techniques for seperating Time and Space complexity classes because we show that: NSPACE[f(n)] ⊆ QR[(f(n))2/log(n)]...
A model is defined in which questions concerning delay bounded asynchronous parallel systems may be investigated. Persistence and determinacy are introduced for this model. These two conditions are shown to be sufficient to guarantee that a synchronous execution policy can be relaxed to an asynchronous execution policy with no change to the result of the computation. In addition, the asynchronous...
This paper describes a new approach to the design of combinational logic using large-scale-integrated (LSI) circuit technology. A simple "prototype" logic function of n binary variables is imbedded within an array of at most (n+1) rows and columns. The cells of this array contain 2-input exclusive-OR gates, and its rows are fed by the input variables and logical "1". Its column...
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