In this paper we investigate in which cases unions of identifiable classes of recursive functions are also necessarily identifiable. We consider identification in the limit with bounds on mindchanges and anomalies. Th...
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ISBN:
(纸本)354065013X
In this paper we investigate in which cases unions of identifiable classes of recursive functions are also necessarily identifiable. We consider identification in the limit with bounds on mindchanges and anomalies. Though not closed under the set union, these identification types still have features resembling closedness. For each of them we find such n that 1) if every union of n - 1 classes out of U-1, ..., U-n is identifiable, so is the union of all n classes;2) there are such classes U-1, ..., Un-1 that every union of n - 2 classes out of them is identifiable, while the union of n - 1 classes is not. We show that by finding these n, we can distinguish which requirements put on the identifiability of unions of classes are satisfiable and which are not. We also show how our problem is connected with team learning.
We present a (relatively) short mechanized proof that Coq types any recursive function which is provably total in Coq. The well-founded (and terminating) induction scheme, which is the foundation of Coq recursion, is ...
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ISBN:
(纸本)9783319661070
We present a (relatively) short mechanized proof that Coq types any recursive function which is provably total in Coq. The well-founded (and terminating) induction scheme, which is the foundation of Coq recursion, is maximal. We implement an unbounded minimization scheme for decidable predicates. It can also be used to reify a whole category of undecidable predicates. This development is purely constructive and requires no axiom. Hence it can be integrated into any project that might assume additional axioms.
A classical learning problem in Inductive Inference consists of identifying each function of a given class of recursive functions from a finite number of its output values. Uniform learning is concerned with the desig...
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ISBN:
(数字)9783540445814
ISBN:
(纸本)3540423435
A classical learning problem in Inductive Inference consists of identifying each function of a given class of recursive functions from a finite number of its output values. Uniform learning is concerned with the design of single programs solving infinitely many classical learning problems. For that purpose the program reads a description of an identification problem and is supposed to construct a technique for solving the particular problem. As can be proved, uniform solvability of collections of solvable identification problems is rather influenced by the description of the problems than by the particular problems themselves. When prescribing a specific inference criterion (for example learning in the limit), a clever choice of descriptions allows uniform solvability of all solvable problems, whereas even the most simple classes of recursive functions are not uniformly learnable without restricting the set of possible descriptions. Furthermore the influence of the hypothesis spaces on uniform learnability is analysed.
This paper deals with a philosophical question that arises within the theory of computational complexity: how to understand the notion of INTRINSIC complexity or difficulty, as opposed to notions of difficulty that de...
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*** [Bar74] has proved that there are classes of total recursive functions which are EX-identifiable but their union is not. We prove that there are no 3 classes U1, U2, U3 such that U1∪U2,U1∪U3 and U2∪U3 would be ...
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We address the problem of proving the equivalence of two recursive functions that have different base-cases and/or are not in lockstep. None of the existing software equivalence checkers (like REVE, RVT, SYMDIFF), or ...
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ISBN:
(纸本)9783319489896;9783319489889
We address the problem of proving the equivalence of two recursive functions that have different base-cases and/or are not in lockstep. None of the existing software equivalence checkers (like REVE, RVT, SYMDIFF), or general unbounded software model-checkers (like SEAHORN, HSFC, AUTOMIZER) can prove such equivalences. We show a proof rule for the case of different base cases, based on separating the proof into two parts-inputs which result in the base case in at least one of the two compared functions, and all the rest. We also show how unbalanced unrolling of the functions can solve the case in which the functions are not in lock-step. In itself this type of unrolling may again introduce the problem of the different base cases, and we show a new proof rule for solving it. We implemented these rules in our regression-verification tool RVT. We conclude by comparing our approach to that of Felsig et al.'s counterexample-based refinement, which was implemented lately in their equivalence checker REVE.
Although the recent popularity of parallel-computing environments has called for parallel programs, it is difficult for nonspecialists to develop those that are efficient. What is required are parallelization methods ...
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ISBN:
(纸本)9783642122507
Although the recent popularity of parallel-computing environments has called for parallel programs, it is difficult for nonspecialists to develop those that are efficient. What is required are parallelization methods that can automatically generate efficient parallel programs from sequential ones. In this paper, we propose an automatic method of parallelization for recursive functions. The key is a quantifier-elimination-based derivation of all operator that shrinks function closures representing partial computations. Once we obtain such an operator, we can split the input structure and perform computation on each part in parallel. Our method has several features: it does not require any human help, it guarantees coniputational efficiency of generated programs, and it deals with complicated recursive functions such as those that are nonlinear recursive, non-self recursive, and accumulative.
We introduce a powerful termination algorithm for structurally recursive functions that improves on the core ideas behind lexicographic termination algorithms for functional programs. The algorithm generates linear-le...
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