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Kötzing, Timo; Schirneck, Martin; Seidel, Karen Normal Forms in Semantic Language Identification. International Conference on Algorithmic Learning Theory (ALT) 2017: 493516
We consider language learning in the limit from text where all learning restrictions are semantic, that is, where any conjecture may be replaced by a semantically equivalent conjecture. For different such learning criteria, starting with the wellknown TxtGBclearning, we consider three different normal forms: strongly locking learning, consistent learning and (partially) setdriven learning. These normal forms support and simplify proofs and give insight into what behaviors are necessary for successful learning (for example when consistency in conservative learning implies cautiousness and strong decisiveness). We show that strongly locking learning can be assumed for partially setdriven learners, even when learning restrictions apply. We give a very general proof relying only on a natural property of the learning restriction, namely, allowing for simulation on equivalent text. Furthermore, when no restrictions apply, also the converse is true: every strongly locking learner can be made partially setdriven. For several semantic learning criteria we show that learning can be done consistently. Finally, we deduce for which learning restrictions partial setdrivenness and setdrivenness coincide, including a general statement about classes of infinite languages. The latter again relies on a simulation argument.

Hölzl, Rupert; Jain, Sanjay; Schlicht, Philipp; Seidel, Karen; Stephan, Frank Automatic Learning from Repetitive Texts. International Conference on Algorithmic Learning Theory (ALT) 2017: 129150
We study the connections between the learnability of automatic families of languages and the types of text used to present them to a learner. More precisely, we study how restrictions on the number of times that a correct datum appears in a text influence what classes of languages are automatically learnable. We show that an automatic family of languages is automatically learnable from fat text iff it is automatically learnable from thick text iff it is verifiable from balanced text iff it satisfies Angluin's telltale condition. Furthermore, many automatic families are automatically learnable from exponential text. We also study the relationship between automatic learnability and verifiability and show that all automatic families are automatically partially verifiable from exponential text and automatically learnable from thick text.

Case, John; Kötzing, Timo Solutions to Open Questions for NonUShaped Learning with Memory Limitations. Algorithmic Learning Theory (ALT) 2010: 285299
A Ushape occurs when a learner first learns, then unlearns, and, finally, relearns, some target concept. Within the framework of Inductive Inference, previous results have shown, for example, that Ushapes are unnecessary for explanatory learning, but are necessary for behaviorally correct learning. This paper solves the following two problems regarding nonUshaped learning posed in the prior literature. First, it is shown that there are classes learnable with three memory states that are not learnable nonUshapedly with any finite number of memory states. This result is surprising, as for learning with one or two memory states, Ushapes are known to be unnecessary. Secondly, it is shown that there is a class learnable memorylessly with a single feedback query such that this class is not learnable nonUshapedly memorylessly with any finite number of feedback queries. This result is complemented by the result that any class of infinite languages learnable memorylessly with finitely many feedback queries is so learnable without Ushapes  in fact, all classes of infinite languages learnable with complete memory are learnable memorylessly with finitely many feedback queries and without Ushapes. On the other hand, we show that there is a class of infinite languages learnable memorylessly with a single feedback query, which is not learnable without Ushapes by any particular bounded number of feedback queries.

Case, John; Kötzing, Timo Dynamically Delayed Postdictive Completeness and Consistency in Learning. Algorithmic Learning Theory (ALT) 2008: 389403
In computational function learning in the limit, an algorithmic learner tries to find a program for a computable function \(g\) given successively more values of \(g\), each time outputting a conjectured program for g. A learner is called postdictively complete iff all available data is correctly postdicted by each conjecture. Akama and Zeugmann presented, for each choice of natural number \(\delta\), a relaxation to postdictive completeness: each conjecture is required to postdict only all except the last \(\delta\) seen data points. This paper extends this notion of delayed postdictive completeness from constant delays to dynamically computed delays. On the one hand, the delays can be different for different data points. On the other hand, delays no longer need to be by a fixed finite number, but any type of computable countdown is allowed, including, for example, countdown in a system of ordinal notations and in other graphs disallowing computable infinitely descending counts. We extend many of the theorems of Akama and Zeugmann and provide some feasible learnability results. Regarding fairness in feasible learning, one needs to limit use of tricks that postpone output hypotheses until there is enough time to “think” about them. We see, for polytime learning, postdictive completeness (and delayed variants): 1. allows some but not all postponement tricks, and 2. there is a surprisingly tight boundary, for polytime learning, between what postponement is allowed and what is not. For example: 1. the set of polytime computable functions is polytime postdictively completely learnable employing some postponement, but 2. the set of exptime computable functions, while polytime learnable with a little more postponement, is not polytime postdictively completely learnable! We have that, for w a notation for \(ømega\), the set of exptime functions is polytime learnable with wdelayed postdictive completeness. Also provided are generalizations to further, small constructive limit ordinals.

Case, John; Kötzing, Timo; Paddock, Todd Feasible Iteration of Feasible Learning Functionals. Algorithmic Learning Theory (ALT) 2007: 3448
For learning functions in the limit, an algorithmic learner obtains successively more data about a function and calculates trials each resulting in the output of a corresponding program, where, hopefully, these programs eventually converge to a correct program for the function. The authors desired to provide a feasible version of this learning in the limit — a version where each trial was conducted feasibly and there was some feasible limit on the number of trials allowed. Employed were basic feasible functionals which query an input function as to its values and which provide each trial. An additional tally argument 0 \(i\) was provided to the functionals for their execution of the \(i\)th trial. In this way more time resource was available for each successive trial. The mechanism employed to feasibly limit the number of trials was to feasibly count them down from some feasible notation for a constructive ordinal. Since all processes were feasible, their termination was feasibly detectable, and, so, it was possible to wait for the trials to terminate and suppress all the output programs but the last. Hence, although there is still an iteration of trials, the learning was a special case of what has long been known as total Finlearning, i.e., learning in the limit, where, on each function, the learner always outputs exactly one conjectured program. Our general main results provide for strict learning hierarchies where the trial count down involves all and only notations for infinite limit ordinals. For our hierarchies featuring finitely many limit ordinal jumps, we have upper and lower total run time bounds of our feasible Finlearners in terms of finite stacks of exponentials. We provide, though, an example of how to regain feasibility by a suitable parameterized complexity analysis.