2019 [ to top ]

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  Fokina, Ekaterina; Kötzing, Timo; San Mauro, Luca Limit Learning Equivalence Structures. Algorithmic Learning Theory (ALT) 2019: 1-20
  [ Abstract ] [ BibTeX ] [ Download ]
   
  While most research in Gold-style learning focuses on learning formal languages, we consider the identification of computable structures, specifically equivalence structures. In our core model the learner gets more and more information about which pairs of elements of a structure are related and which are not. The aim of the learner is to find (an effective description of) the isomorphism type of the structure presented in the limit. In accordance with language learning we call this learning criterion InfEx-learning (explanatory learning from informant). We start with a discussion and separations of different variants of this learning criterion, including learning from text (where the only information provided is which elements are related, and not which elements are not related) and finite learning (where the first actual conjecture of the learner has to be correct). This gives first intuitions and examples for what (classes of) structures are learnable and which are not. Our main contribution is a complete characterization of the learnable classes of structures in terms of a combinatorial property of the classes. This property allows us to derive a bound of \(\mathbf{0''}\) on the computational complexity required to learn uniformly enumerable classes of structures. Finally, we show how learning classes of structures relates to learning classes of languages by mapping learning tasks for structures to equivalent learning tasks for languages.
  @inproceedings{fokina2019limit, abstract = {While most research in Gold-style learning focuses on learning formal languages, we consider the identification of computable structures, specifically equivalence structures. In our core model the learner gets more and more information about which pairs of elements of a structure are related and which are not. The aim of the learner is to find (an effective description of) the isomorphism type of the structure presented in the limit. In accordance with language learning we call this learning criterion InfEx-learning (explanatory learning from informant). We start with a discussion and separations of different variants of this learning criterion, including learning from text (where the only information provided is which elements are related, and not which elements are not related) and finite learning (where the first actual conjecture of the learner has to be correct). This gives first intuitions and examples for what (classes of) structures are learnable and which are not. Our main contribution is a complete characterization of the learnable classes of structures in terms of a combinatorial property of the classes. This property allows us to derive a bound of \(\mathbf{0''}\) on the computational complexity required to learn uniformly enumerable classes of structures. Finally, we show how learning classes of structures relates to learning classes of languages by mapping learning tasks for structures to equivalent learning tasks for languages.}, author = {Fokina, Ekaterina and Kötzing, Timo and San Mauro, Luca}, booktitle = {Algorithmic Learning Theory (ALT)}, keywords = {alt ekaterinafokina lucasanmauro timokoetzing year2019}, pages = {1-20}, title = {Limit Learning Equivalence Structures}, volume = 98, year = 2019 }

2017 [ to top ]

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  Kötzing, Timo; Schirneck, Martin; Seidel, Karen Normal Forms in Semantic Language Identification. Algorithmic Learning Theory (ALT) 2017: 493-516
  [ Abstract ] [ BibTeX ] [ URL ] [ Download ]
   
  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 well-known TxtGBc-learning, we consider three different normal forms: strongly locking learning, consistent learning and (partially) set-driven 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 set-driven 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 set-driven. For several semantic learning criteria we show that learning can be done consistently. Finally, we deduce for which learning restrictions partial set-drivenness and set-drivenness coincide, including a general statement about classes of infinite languages. The latter again relies on a simulation argument.
  @inproceedings{DBLP:conf/alt/KotzingSS17, abstract = {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 well-known TxtGBc-learning, we consider three different normal forms: strongly locking learning, consistent learning and (partially) set-driven 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 set-driven 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 set-driven. For several semantic learning criteria we show that learning can be done consistently. Finally, we deduce for which learning restrictions partial set-drivenness and set-drivenness coincide, including a general statement about classes of infinite languages. The latter again relies on a simulation argument.}, author = {Kötzing, Timo and Schirneck, Martin and Seidel, Karen}, booktitle = {Algorithmic Learning Theory (ALT)}, keywords = {alt karenseidel martinschirneck timokoetzing year2017}, pages = {493-516}, title = {Normal Forms in Semantic Language Identification}, year = 2017 }
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  Hölzl, Rupert; Jain, Sanjay; Schlicht, Philipp; Seidel, Karen; Stephan, Frank Automatic Learning from Repetitive Texts. Algorithmic Learning Theory (ALT) 2017: 129-150
  [ Abstract ] [ BibTeX ] [ URL ] [ Download ]
   
  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 tell-tale 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.
  @inproceedings{DBLP:conf/alt/HolzlJSS017, abstract = {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 tell-tale 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.}, author = {H{{ö}}lzl, Rupert and Jain, Sanjay and Schlicht, Philipp and Seidel, Karen and Stephan, Frank}, booktitle = {Algorithmic Learning Theory (ALT)}, keywords = {alt frankstephan karenseidel philippschlicht ruperthoelzl sanjayjain year2017}, pages = {129-150}, title = {Automatic Learning from Repetitive Texts}, year = 2017 }

2011 [ to top ]

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  Kötzing, Timo Iterative Learning from Positive Data and Counters. Algorithmic Learning Theory (ALT) 2011: 40-54
  [ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
   
  We analyze iterative learning in the limit from positive data with the additional information provided by a counter. The simplest type of counter provides the current iteration number (counting up from 0 to infinity), which is known to improve learning power over plain iterative learning. We introduce five other (weaker) counter types, for example only providing some unbounded and non-decreasing sequence of numbers. Analyzing these types allows one to understand which properties of a counter learning can benefit from. For the iterative setting, we completely characterize the relative power of the learning criteria corresponding to the counter types. In particular, for our types, the only properties improving learning power are unboundedness and strict monotonicity. Furthermore, we show that each of our types of counter improves learning power over weaker ones in some settings; to this end, we analyze transductive and non-U-shaped learning. Finally we show that, for iterative learning criteria with one of our types of counter, separations of learning criteria are necessarily witnessed by classes containing only infinite languages.
  @inproceedings{DBLP:conf/alt/Kotzing11, abstract = {We analyze iterative learning in the limit from positive data with the additional information provided by a counter. The simplest type of counter provides the current iteration number (counting up from 0 to infinity), which is known to improve learning power over plain iterative learning. We introduce five other (weaker) counter types, for example only providing some unbounded and non-decreasing sequence of numbers. Analyzing these types allows one to understand which properties of a counter learning can benefit from. For the iterative setting, we completely characterize the relative power of the learning criteria corresponding to the counter types. In particular, for our types, the only properties improving learning power are unboundedness and strict monotonicity. Furthermore, we show that each of our types of counter improves learning power over weaker ones in some settings; to this end, we analyze transductive and non-U-shaped learning. Finally we show that, for iterative learning criteria with one of our types of counter, separations of learning criteria are necessarily witnessed by classes containing only infinite languages.}, author = {Kötzing, Timo}, booktitle = {Algorithmic Learning Theory (ALT)}, keywords = {alt timokoetzing year2011}, pages = {40-54}, title = {Iterative Learning from Positive Data and Counters}, year = 2011 }

2010 [ to top ]

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  Case, John; Kötzing, Timo Solutions to Open Questions for Non-U-Shaped Learning with Memory Limitations. Algorithmic Learning Theory (ALT) 2010: 285-299
  [ Abstract ] [ BibTeX ] [ DOI ] [ Download ]
   
  A U-shape 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 U-shapes are unnecessary for explanatory learning, but are necessary for behaviorally correct learning. This paper solves the following two problems regarding non-U-shaped learning posed in the prior literature. First, it is shown that there are classes learnable with three memory states that are not learnable non-U-shapedly with any finite number of memory states. This result is surprising, as for learning with one or two memory states, U-shapes 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 non-U-shapedly 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 U-shapes - in fact, all classes of infinite languages learnable with complete memory are learnable memorylessly with finitely many feedback queries and without U-shapes. 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 U-shapes by any particular bounded number of feedback queries.
  @inproceedings{DBLP:conf/alt/CaseK10, abstract = {A U-shape 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 U-shapes are unnecessary for explanatory learning, but are necessary for behaviorally correct learning. This paper solves the following two problems regarding non-U-shaped learning posed in the prior literature. First, it is shown that there are classes learnable with three memory states that are not learnable non-U-shapedly with any finite number of memory states. This result is surprising, as for learning with one or two memory states, U-shapes 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 non-U-shapedly 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 U-shapes - in fact, all classes of infinite languages learnable with complete memory are learnable memorylessly with finitely many feedback queries and without U-shapes. 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 U-shapes by any particular bounded number of feedback queries.}, author = {Case, John and Kötzing, Timo}, booktitle = {Algorithmic Learning Theory (ALT)}, keywords = {alt imported johncase timokoetzing year2010}, pages = {285-299}, publisher = {Springer}, series = {Lecture Notes in Computer Science}, title = {Solutions to Open Questions for Non-U-Shaped Learning with Memory Limitations}, volume = 6331, year = 2010 }

2008 [ to top ]

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  Case, John; Kötzing, Timo Dynamically Delayed Postdictive Completeness and Consistency in Learning. Algorithmic Learning Theory (ALT) 2008: 389-403
  [ Abstract ] [ BibTeX ] [ DOI ] [ Download ]
   
  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 w-delayed postdictive completeness. Also provided are generalizations to further, small constructive limit ordinals.
  @inproceedings{DBLP:conf/alt/CaseK08, abstract = {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 w-delayed postdictive completeness. Also provided are generalizations to further, small constructive limit ordinals.}, author = {Case, John and Kötzing, Timo}, booktitle = {Algorithmic Learning Theory (ALT)}, keywords = {alt imported johncase timokoetzing year2008}, pages = {389-403}, publisher = {Springer}, series = {Lecture Notes in Computer Science}, title = {Dynamically Delayed Postdictive Completeness and Consistency in Learning}, volume = 5254, year = 2008 }

2007 [ to top ]

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  Case, John; Kötzing, Timo; Paddock, Todd Feasible Iteration of Feasible Learning Functionals. Algorithmic Learning Theory (ALT) 2007: 34-48
  [ Abstract ] [ BibTeX ] [ DOI ] [ Download ]
   
  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 Fin-learning, 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 Fin-learners in terms of finite stacks of exponentials. We provide, though, an example of how to regain feasibility by a suitable parameterized complexity analysis.
  @inproceedings{DBLP:conf/alt/CaseKP07, abstract = {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 Fin-learning, 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 Fin-learners in terms of finite stacks of exponentials. We provide, though, an example of how to regain feasibility by a suitable parameterized complexity analysis.}, author = {Case, John and Kötzing, Timo and Paddock, Todd}, booktitle = {Algorithmic Learning Theory (ALT)}, keywords = {alt imported timokoetzing toddpaddock year2007}, pages = {34-48}, publisher = {Springer}, series = {Lecture Notes in Computer Science}, title = {Feasible Iteration of Feasible Learning Functionals}, volume = 4754, year = 2007 }