Schizophrenia patients consistently show deficits on tasks of explicit learning and memory. In contrast, their performance on implicit processing tasks often appears to be relatively intact, though most studies have focused on implicit learning of motor skills. This study evaluated implicit learning in 59 medicated schizophrenia outpatients and 43 healthy controls using two different cognitive skill tasks. Participants completed a Probabilistic Classification task to assess procedural habit learning and an Artificial Grammar task to assess incidental learning of complex rule-based knowledge, as well as an explicit verbal learning and memory task. In addition to performing worse than controls on the explicit learning task, patients showed worse overall performance on the Probabilistic Classification task, which involves gradual learning through trial-by-trial performance feedback. However, patients and controls showed similar levels of learning on the Artificial Grammar task, suggesting a preserved ability to acquire complex rule-based knowledge in the absence of performance feedback. Discussion focuses on possible explanations for schizophrenia patients’ poor Probabilistic Classification task performance.
schizophrenia; implicit learning; neurocognition; habit learning
To avoid some conceptual and methodological pitfalls found in traditional artificial grammar learning tasks, we developed a new method of measuring implicit learning using immediate memory span. Subjects were presented with sequences generated by an artificial grammar and were asked to reproduce the patterns by pressing buttons on a response box. After exposure to these sequences, subjects showed selective improvement in immediate memory span for novel sequences governed by the same grammar. Individual differences in implicit learning covaried with measures of auditory digit span. Subjects with greater immediate memory processing capacity were better able to learn and subsequently exploit the information available in grammatical sequences. Our results are consistent with a detailed episodic coding framework in which implicit learning occurs as an incidental by-product of explicit task performance. Although subjects encode highly detailed information about specific instances, they use different aspects of this information to accomplish different task-specific demands.
Typically developing children aged 5 to 8 years were exposed to artificial grammar learning. Following an implicit exposure phase, half of the participants received neutral instructions at test while the other half received instructions making a direct, explicit reference to the training phase. We first aimed to assess whether implicit learning operated in the two test conditions. We then evaluated the differential impact of age on learning performances as a function of test instructions. The results showed that performance did not vary as a function of age in the implicit instructions condition, while age effects emerged when explicit instructions were employed at test. However, performance was affected differently by age and the instructions given at test, depending on whether the implicit learning of short or long units was assessed. These results suggest that the claim that the implicit learning process is independent of age needs to be revised.
In the current paper, we first evaluate the suitability of traditional serial
reaction time (SRT) and artificial grammar learning (AGL) experiments for
measuring implicit learning of social signals. We then report the results of a
novel sequence learning task which combines aspects of the SRT and AGL paradigms
to meet our suggested criteria for how implicit learning experiments can be
adapted to increase their relevance to situations of social intuition. The
sequences followed standard finite-state grammars. Sequence learning and
consciousness of acquired knowledge were compared between 2 groups of 24
participants viewing either sequences of individually presented letters or
sequences of body-posture pictures, which were described as series of yoga
movements. Participants in both conditions showed above-chance classification
accuracy, indicating that sequence learning had occurred in both stimulus
conditions. This shows that sequence learning can still be found when learning
procedures reflect the characteristics of social intuition. Rule awareness was
measured using trial-by-trial evaluation of decision strategy (Dienes & Scott, 2005; Scott & Dienes, 2008). For letters,
sequence classification was best on trials where participants reported
responding on the basis of explicit rules or memory, indicating some explicit
learning in this condition. For body-posture, classification was not above
chance on these types of trial, but instead showed a trend to be best on those
trials where participants reported that their responses were based on intuition,
familiarity, or random choice, suggesting that learning was more implicit.
Results therefore indicate that the use of traditional stimuli in research on
sequence learning might underestimate the extent to which learning is implicit
in domains such as social learning, contributing to ongoing debate about
levels of conscious awareness in implicit learning.
implicit learning; social intuition; intuition; artificial grammar learning; human movement; consciousness; fringe consciousness
Are explicit versus implicit learning mechanisms reflected in the brain as distinct neural structures, as previous research indicates, or are they distinguished by brain networks that involve overlapping systems with differential connectivity? In this functional MRI study we examined the neural correlates of explicit and implicit learning of artificial grammar sequences. Using effective connectivity analyses we found that brain networks of different connectivity underlie the two types of learning: while both processes involve activation in a set of cortical and subcortical structures, explicit learners engage a network that uses the insula as a key mediator whereas implicit learners evoke a direct frontal-striatal network. Individual differences in working memory also differentially impact the two types of sequence learning.
The present study examined the impact of engaging frontal-mediated, working memory processes on implicit and explicit category learning. Two stimulus dimensions were relevant to categorization, but in some conditions a third irrelevant dimension was also presented. Results indicated that, in both implicit and explicit conditions, the inclusion of the irrelevant dimension impaired performance by increasing the reliance on sub-optimal unidimensional strategies. With three-dimension stimuli a striking dissociation was observed between implicit and explicit category learning when participants performed the sequential working memory task. With explicit category learning, performance was impaired further and there was an increased use of sub-optimal unidimensional strategies. However, with implicit category learning, the performance impairment decreased and there was an increased use of optimal strategies. These findings demonstrate the paradoxical situation in which learning can be improved under sequential-task conditions and have important implications for training, decision making, and understanding interactive memory systems.
Implicit learning is often assumed to be an effortless process. However, some
artificial grammar learning and sequence learning studies using dual tasks seem
to suggest that attention is essential for implicit learning to occur. This
discrepancy probably results from the specific type of secondary task that is
used. Different secondary tasks may engage attentional resources differently and
therefore may bias performance on the primary task in different ways. Here, we
used a random number generation (RNG) task, which may allow for a closer
monitoring of a participant’s engagement in a secondary task than the popular
secondary task in sequence learning studies: tone counting (TC). In the first
two experiments, we investigated the interference associated with performing RNG
concurrently with a serial reaction time (SRT) task. In a third experiment, we
compared the effects of RNG and TC. In all three experiments, we directly
evaluated participants’ knowledge of the sequence with a subsequent sequence
generation task. Sequence learning was consistently observed in all experiments,
but was impaired under dual-task conditions. Most importantly, our data suggest
that RNG is more demanding and impairs learning to a greater extent than TC.
Nevertheless, we failed to observe effects of the secondary task in subsequent
sequence generation. Our studies indicate that RNG is a promising task to
explore the involvement of attention in the SRT task.
implicit learning; attention; serial reaction time task; random number generation task; tone counting task
Context-free grammars are fundamental for the description of linguistic syntax. However, most artificial grammar learning experiments have explored learning of simpler finite-state grammars, while studies exploring context-free grammars have not assessed awareness and implicitness. This paper explores the implicit learning of context-free grammars employing features of hierarchical organization, recursive embedding and long-distance dependencies. The grammars also featured the distinction between left- and right-branching structures, as well as between centre- and tail-embedding, both distinctions found in natural languages. People acquired unconscious knowledge of relations between grammatical classes even for dependencies over long distances, in ways that went beyond learning simpler relations (e.g. n-grams) between individual words. The structural distinctions drawn from linguistics also proved important as performance was greater for tail-embedding than centre-embedding structures. The results suggest the plausibility of implicit learning of complex context-free structures, which model some features of natural languages. They support the relevance of artificial grammar learning for probing mechanisms of language learning and challenge existing theories and computational models of implicit learning.
OBJECTIVE: To determine whether memory data presented for a schizophrenia sample in the Technical Manual of the Wechsler Memory Scale-Third Edition support trends identified in a previously published review of studies employing an earlier version of the instrument, the Wechsler Memory Scale-Revised. DESIGN: Archival: reformulation of published data. PATIENTS: Patients with schizophrenia, Alzheimer's disease, Korsakoff's syndrome or traumatic brain injury (TBI) for whom intelligence and memory data were reported in the Technical Manual of the Wechsler Adult Intelligence Scale-Third Edition Wechsler Memory Scale-Third Edition (WAIS-III WMS-III). OUTCOME MEASURES: Mean Full Scale, Verbal, and Performance Intelligence Quotients of the WAIS-III and mean WMS-III Immediate and General Memory Indexes. Single-trial learning and learning slope data were also culled from the WAIS-III WMS-III Technical Manual. RESULTS: Memory indexes for patients with Alzheimer's disease or Korsakoff's syndrome were substantially lower than those for patients with schizophrenia or TBI. In tests of learning processes, patients with schizophrenia had an inferior ability to repeat material presented just once, in comparison with the standardization sample. However, they did relatively better with repeated presentations than patients with Alzheimer's disease or Korsakoff's syndrome. The learning slope for patients with schizophrenia demonstrated an ability to absorb and consolidate increasing amounts of material with repeated exposure that is inconsistent with pronounced memory impairment. CONCLUSIONS: Although patients with schizophrenia exhibit new learning deficiencies, their memory capabilities are not substantially weaker than their general intellectual abilities, and do not approach the memory impairment exhibited by patients with Alzheimer's disease or Korsakoff's syndrome.
Natural number arithmetic is a simple, powerful and important symbolic system. Despite intense focus on learning in cognitive development and educational research many adults have weak knowledge of the system. In current study participants learn arithmetic principles via an implicit learning paradigm. Participants learn not by solving arithmetic equations, but through viewing and evaluating example equations, similar to the implicit learning of artificial grammars. We expand this to the symbolic arithmetic system. Specifically we find that exposure to principle-inconsistent examples facilitates the acquisition of arithmetic principle knowledge if the equations are presented to the learning in a temporally proximate fashion. The results expand on research of the implicit learning of regularities and suggest that contrasting cases, show to facilitate explicit arithmetic learning, is also relevant to implicit learning of arithmetic.
The domain of syntax is seen as the core of the language faculty and as the most critical difference between animal vocalizations and language. We review evidence from spontaneously produced vocalizations as well as from perceptual experiments using artificial grammars to analyse animal syntactic abilities, i.e. abilities to produce and perceive patterns following abstract rules. Animal vocalizations consist of vocal units (elements) that are combined in a species-specific way to create higher order strings that in turn can be produced in different patterns. While these patterns differ between species, they have in common that they are no more complex than a probabilistic finite-state grammar. Experiments on the perception of artificial grammars confirm that animals can generalize and categorize vocal strings based on phonetic features. They also demonstrate that animals can learn about the co-occurrence of elements or learn simple ‘rules’ like attending to reduplications of units. However, these experiments do not provide strong evidence for an ability to detect abstract rules or rules beyond finite-state grammars. Nevertheless, considering the rather limited number of experiments and the difficulty to design experiments that unequivocally demonstrate more complex rule learning, the question of what animals are able to do remains open.
birdsong; artificial grammar learning; syntax; language; vocalization; rule learning
Patients with amnesia have deficits in declarative memory but intact memory for motor and perceptual skills, which suggests that explicit memory and implicit memory are distinct. However, the evidence that implicit motor learning is intact in amnesic patients is contradictory. This study investigated implicit sequence learning in amnesic patients with Korsakoff’s syndrome (N = 20) and matched controls (N = 14), using the classical Serial Reaction Time Task and a newly developed Pattern Learning Task in which the planning and execution of the responses are more spatially demanding. Results showed that implicit motor learning occurred in both groups of participants; however, on the Pattern Learning Task, the percentage of errors did not increase in the Korsakoff group in the random test phase, which is indicative of less implicit learning. Thus, our findings show that the performance of patients with Korsakoff’s syndrome is compromised on an implicit learning task with a strong spatial response component.
Korsakoff’s syndrome; Amnesia; Implicit learning; Motor learning; Sequence learning; Memory
It is widely believed that adults cannot learn a foreign language in the same way that children learn a first language. However, recent evidence suggests that adult learners of a foreign language can come to rely on native-like language brain mechanisms. Here, we show that the type of language training crucially impacts this outcome. We used an artificial language paradigm to examine longitudinally whether explicit training (that approximates traditional grammar-focused classroom settings) and implicit training (that approximates immersion settings) differentially affect neural (electrophysiological) and behavioral (performance) measures of syntactic processing. Results showed that performance of explicitly and implicitly trained groups did not differ at either low or high proficiency. In contrast, electrophysiological (ERP) measures revealed striking differences between the groups’ neural activity at both proficiency levels in response to syntactic violations. Implicit training yielded an N400 at low proficiency, whereas at high proficiency, it elicited a pattern typical of native speakers: an anterior negativity followed by a P600 accompanied by a late anterior negativity. Explicit training, by contrast, yielded no significant effects at low proficiency and only an anterior positivity followed by a P600 at high proficiency. Although the P600 is reminiscent of native-like processing, this response pattern as a whole is not. Thus, only implicit training led to an electrophysiological signature typical of native speakers. Overall, the results suggest that adult foreign language learners can come to rely on native-like language brain mechanisms, but that the conditions under which the language is learned may be crucial in attaining this goal.
AIM: To investigate cognitive functioning and depressive symptoms in adolescents with inflammatory bowel disease (IBD).
METHODS: A neuropsychological test battery, including subtests of the Wechsler Adult Intelligence Scale-Revised and III, Wechsler Memory Scale-Revised, California Verbal Learning Test (CVLT), Stroop Color-Word Test, and Trail Making Test, which assessed verbal and visual short- and long-term memory, processing speed, logical reasoning, verbal intelligence, attention, and executive functioning, was administered to 13- to 19-year-old patients with IBD (n = 34; active disease n = 20). Depressive symptoms were measured with the Beck Depression Inventory. The findings were compared with peers with non-acute juvenile idiopathic arthritis (JIA; n = 23). Patients with coexisting psychiatric disorders were excluded.
RESULTS: The IBD group, especially patients in the acute phase, made more perseverative errors in the CVLT test that assessed verbal memory than the JIA group (6.0 ± 4.3 vs 3.3 ± 2.9, P < 0.01), but no other differences between the IBD and JIA groups were observed in the neuropsychological tests. The difference was close to statistical significance, even when glucocorticoid medication was controlled for (P < 0.052). The IBD group had more depressive symptoms than the JIA group (7.9 ± 7.6 vs 4.0 ± 4.0, P < 0.05). Approximately one third of the IBD group had at least mild depressive symptoms, and those with acute illness had the highest scores. However, depressive symptoms were not related to the difference in the verbal memory test (perseverative errors in the CVLT) between the IBD and JIA groups.
CONCLUSION: Adolescents with acute IBD may have mild verbal memory problems but no major cognitive deficits compared to peers with JIA.
Cognitive impairment; Inflammatory bowel disease; Crohn’s disease; Depressive symptoms; Ulcerative colitis; Adolescents
In the present experiment, we used event-related potentials (ERP) to investigate the role of immediate and delayed feedback in an artificial grammar learning (AGL) task. Two groups of participants were engaged in classifying non-word strings according to an underlying rule system, not known to the participants. Visual feedback was provided after each classification either immediately or with a short delay of 1 s. Both groups were able to learn the artificial grammar system as indicated by an increase in classification performance. However, the gain in performance was significantly larger for the group receiving immediate feedback as compared to the group receiving delayed feedback. Learning was accompanied by an increase in P300 activity in the ERP for delayed as compared to immediate feedback. Irrespective of feedback delay, both groups exhibited learning related decreases in the feedback-related positivity (FRP) elicited by positive feedback only. The feedback-related negativity (FRN), however, remained constant over the course of learning. These results suggest, first, that delayed feedback is less effective for AGL as task requirements are very demanding, and second, that the FRP elicited by positive prediction errors decreases with learning while the FRN to negative prediction errors is elicited in an all-or-none fashion by negative feedback throughout the entire experiment.
artificial grammar learning; ERN; feedback positivity; delayed feedback
Considerable evidence suggests that people acquire artificial grammars incidentally and implicitly, an indispensable capacity for the acquisition of music or language. However, less research has been devoted to exploring constraints affecting incidental learning. Within the domain of music, the extent to which Narmour's (1990) melodic principles affect implicit learning of melodic structure was experimentally explored. Extending previous research (Rohrmeier, Rebuschat & Cross, 2011), the identical finite-state grammar is employed having terminals (the alphabet) manipulated so that melodies generated systematically violated Narmour's principles. Results indicate that Narmour-inconsistent melodic materials impede implicit learning. This further constitutes a case in which artificial grammar learning is affected by prior knowledge or processing constraints.
Patients with comorbid schizophrenia and panic symptoms share a distinct clinical presentation and biological characteristics, prompting some to propose panic psychosis as a separate subtype of schizophrenia. Less is known about these patients’ neuropsychological profiles, knowledge of which may facilitate target-specific treatments and research into the etiopathophysiology for such cases. A total of 255 schizophrenia patients with panic disorder (n=39), non-panic anxiety disorder (n=51), or no anxiety disorder (n=165) were assessed with the Wechsler Adult Intelligence Scale – Revised, the Wisconsin Card Sorting Test, the Trail Making Test, the Controlled Oral Word Association Test, the Animal Naming subtest of the Boston Diagnostic Aphasia Examination, and the Wechsler Memory Scale – Revised. Psychotic symptoms were assessed with the Positive and Negative Syndrome Scale. Patients with panic disorder demonstrated a higher verbal IQ and better problem solving, set switching, delayed recall, attention, and verbal fluency as compared to schizophrenia patients without comorbid anxiety. The schizophrenia-panic group reported a higher level of dysthymia on stable medication. Our findings suggest that patients with schizophrenia and comorbid panic disorder exhibit distinct cognitive functioning when compared to other schizophrenia patients. These data offer further support for a definable panic-psychosis subtype and suggest new etiological pathways for future research.
schizophrenia; schizoaffective disorder; psychosis; panic disorder; anxiety disorder; neuropsychological profile; cognitive functioning
We used a prototype extraction task to assess implicit learning of a meaningful novel visual category. Cortical activation was monitored in young adults with functional magnetic resonance imaging. We observed occipital deactivation at test consistent with perceptually based implicit learning, and lateral temporal cortex deactivation reflecting implicit acquisition of the category's semantic nature. Medial temporal lobe (MTL) activation during exposure and test suggested involvement of explicit memory as well. Behavioral performance of Alzheimer's disease (AD) patients and healthy seniors was also assessed, and AD performance was correlated with gray matter volume using voxel-based morphometry. AD patients showed learning, consistent with preserved implicit memory, and confirming that AD patients' implicit memory is not limited to abstract patterns. However, patients were somewhat impaired relative to healthy seniors. Occipital and lateral temporal cortical volume correlated with successful AD patient performance, and thus overlapped with young adults' areas of deactivation. Patients' severe MTL atrophy precluded involvement of this region. AD patients thus appear to engage a cortically based implicit memory mechanism, whereas their relative deficit on this task may reflect their MTL disease. These findings suggest that implicit and explicit memory systems collaborate in neurologically intact individuals performing an ostensibly implicit memory task.
Alzheimer's; explicit memory; fMRI; implicit memory; medial temporal
A study combining artificial grammar and sentence comprehension methods investigated the learning and online use of probabilistic, nonadjacent combinatorial constraints. Participants learned a small artificial language describing cartoon monsters acting on objects. Self-paced reading of sentences in the artificial language revealed comprehenders' sensitivity to nonadjacent combinatorial constraints, without explicit awareness of the probabilities embedded in the language. These results show that even newly-learned constraints have a an identifiable effect on online sentence processing. The rapidity of learning in this paradigm relative to others has implications for theories of implicit learning and its role in language acquisition.
Considerable individual differences in language ability exist among normally developing children and adults. Whereas past research have attributed such differences to variations in verbal working memory or experience with language, we test the hypothesis that individual differences in statistical learning may be associated with differential language performance. We employ a novel paradigm for studying statistical learning on-line, combining a serial-reaction time task with artificial grammar learning. This task offers insights into both the timecourse of and individual differences in statistical learning. Experiment 1 charts the micro-level trajectory for statistical learning of nonadjacent dependencies and provides an on-line index of individual differences therein. In Experiment 2, these differences are then shown to predict variations in participants’ on-line processing of long-distance dependencies involving center-embedded relative clauses. The findings suggest that individual differences in the ability to learn from experience through statistical learning may contribute to variations in linguistic performance.
statistical learning; language processing; individual differences; serial-reaction time; artificial grammar; relative clauses
Researchers disagree about why patients with schizophrenia perform poorly on memory tests. Some argue the presence of a fundamental memory deficit stemming from dysfunction in medial temporal lobe structures, principally the hippocampus. Others, stressing the contributions of impaired attention or executive failings such as a disorganized approach to learning, implicate larger neural networks. We compared data from psychometrically similar procedures, the Wechsler Memory Scale-Revised (WMS-R) and Wechsler Adult Intelligence Scale-Revised (WAIS-R), generated by 17 schizophrenia-spectrum patients and 33 psychiatric controls. We then compared our findings in detail with all published WMS-R/WAIS-R schizophrenia data. Our findings and the literature indicate that the acquisition of new information is disrupted in schizophrenia, but they provide little support for claims that memory deficits are especially pronounced relative to other weaknesses. Since schizophrenia patients exhibit reasonable retention following intervening activity, theories that place primary emphasis upon hippocampal dysfunction are not well supported.
Recent studies have reported abnormal implicit learning of sequential patterns in patients with schizophrenia. Because these studies were based on visuospatial cues, the question remained whether patients were impaired simply due to the demands of spatial processing. This study examined implicit sequence learning in 24 patients with schizophrenia and 24 healthy controls using a non-spatial variation of the serial reaction time test (SRT) in which pattern stimuli alternated with random stimuli on every other trial. Both groups showed learning by responding faster and more accurately to pattern trials than to random trials. Patients, however, showed a smaller magnitude of sequence learning. Both groups were unable to demonstrate explicit knowledge of the nature of the pattern, confirming that learning occurred without awareness. Clinical variables were not correlated with the patients' learning deficits. Patients with schizophrenia have a decreased ability to develop sensitivity to regularly occurring sequences of events within their environment. This type of deficit may affect an array of cognitive and motor functions that rely on the perception of event regularity.
Serial learning; Motor skills; Cognition; Psychiatry; Memory; Behavior
We investigated the neurocognitive deficits in schizophrenic patients with and without obsessive-compulsive disorder (OCD).
We grouped 27 patients as either obsessive-compulsive or non-obsessive-compulsive based on the presence of OCD. The two groups completed the Yale-Brown Obsessive-Compulsive Scale (Y-BOCS), Positive and Negative Symptom Scale (PANSS), and Hamilton Depression Scale. The intelligence quotient (IQ) was tested using the Korean Wechsler Adult Intelligence Scale. The memory quotient (MQ) was tested using the Korean-Auditory Verbal Learning and Korean-Complex Figure Test. The executive intelligence quotient (EIQ) was determined using the Kims executive intelligence test (EXIT).
Ten of the 27 patients had OCD. The compulsion score of Y-BOCS was positively correlated with positive symptoms, negative symptoms, and the total scores of PANSS. The OCD-schizophrenia patients had higher IQs. No difference was found in MQ. Although the EIQ did not differ between the two groups, the OCD-schizophrenia patients performed better at the Stroop-interference and verbal fluency tests, which was highly dependent on executive function.
Our findings suggest that OCD may have a protective effect on some cognitive function, at least in relatively early stage of illness. Moreover, based on clinical, neurocognitive features, schizophrenia with OCD could be considered as a distinct subtype of schizophrenia.
Schizophrenia; Obsessive compulsive disorder; Cognitive function
Artificial grammar learning (AGL) provides a useful tool for exploring rule learning strategies linked to general purpose pattern perception. To be able to directly compare performance of humans with other species with different memory capacities, we developed an AGL task in the visual domain. Presenting entire visual patterns simultaneously instead of sequentially minimizes the amount of required working memory. This approach allowed us to evaluate performance levels of two bird species, kea (Nestor notabilis) and pigeons (Columba livia), in direct comparison to human participants. After being trained to discriminate between two types of visual patterns generated by rules at different levels of computational complexity and presented on a computer screen, birds and humans received further training with a series of novel stimuli that followed the same rules, but differed in various visual features from the training stimuli. Most avian and all human subjects continued to perform well above chance during this initial generalization phase, suggesting that they were able to generalize learned rules to novel stimuli. However, detailed testing with stimuli that violated the intended rules regarding the exact number of stimulus elements indicates that neither bird species was able to successfully acquire the intended pattern rule. Our data suggest that, in contrast to humans, these birds were unable to master a simple rule above the finite-state level, even with simultaneous item presentation and despite intensive training.
artificial grammar learning; formal language theory; pattern learning; visual stimuli; simultaneous presentation; comparative research
A bisection-type algorithm for the grammar-based compression of tree-structured data has been proposed recently. In this framework, an elementary ordered-tree grammar (EOTG) and an elementary unordered-tree grammar (EUTG) were defined, and an approximation algorithm was proposed.
In this paper, we propose an integer programming-based method that finds the minimum context-free grammar (CFG) for a given string under the condition that at most two symbols appear on the right-hand side of each production rule. Next, we extend this method to find the minimum EOTG and EUTG grammars for given ordered and unordered trees, respectively. Then, we conduct computational experiments for the ordered and unordered artificial trees. Finally, we apply our methods to pattern extraction of glycan tree structures.
We propose integer programming-based methods that find the minimum CFG, EOTG, and EUTG for given strings, ordered and unordered trees. Our proposed methods for trees are useful for extracting patterns of glycan tree structures.