Todd Wareham

Parameterized Complexity in Cognitive Modeling

In cognitive science, natural cognitive processes are generally conceptualized as computational processes: they serve to transform sensory and mental inputs into mental and action outputs. At the highest level of abstraction, computational models of cognitive processes aim at specifying the computational problem computed by the process under study. Because computational problems are realistic cognitive models only insofar as they can plausibly be computed by the human brain given its limited resources for computation, computational tractability provides a useful constraint on cognitive models. In this paper, we consider the particular benefits of the parameterized complexity framework for identifying sources of intractability in cognitive models. We review existing applications of the parameterized framework to this end in the domains of perception, action and higher cognition. We further identify important opportunities and challenges for future research. These include the development of new methods for complexity analyses specifically tailored to the reverse engineering perspective underlying cognitive science.

Ancestral maximum likelihood of evolutionary trees is hard.

Maximum likelihood (ML) (Neyman, 1971) is an increasingly popular optimality criterion for selecting evolutionary trees. Finding optimal ML trees appears to be a very hard computational task--in particular, algorithms and heuristics for ML take longer to run than algorithms and heuristics for maximum parsimony (MP). However, while MP has been known to be NP-complete for over 20 years, no such hardness result has been obtained so far for ML. In this work we make a first step in this direction by proving that ancestral maximum likelihood (AML) is NP-complete. The input to this problem is a set of aligned sequences of equal length and the goal is to find a tree and an assignment of ancestral sequences for all of that trees internal vertices such that the likelihood of generating both the ancestral and contemporary sequences is maximized. Our NP-hardness proof follows that for MP given in (Day, Johnson and Sankoff, 1986) in that we use the same reduction from Vertex Cover; however, the proof of correctness for this reduction relative to AML is different and substantially more involved.

Intractability and the use of heuristics in psychological explanations

Many cognitive scientists, having discovered that some computational-level characterization f of a cognitive capacity

Ancestral Maximum Likelihood of Evolutionary Trees Is Hard

{\phi}

Ignorance is bliss: A complexity perspective on adapting reactive architectures

is intractable, invoke heuristics as algorithmic-level explanations of how cognizers compute f. We argue that such explanations are actually dysfunctional, and rebut five possible objections. We then propose computational-level theory revision as a principled and workable alternative.

Rational analysis, intractability, and the prospects of 'as if'-explanations

Human intentional communication is marked by its flexibility and context sensitivity. Hypothesized brain mechanisms can provide convincing and complete explanations of the human capacity for intentional communication only insofar as they can match the computational power required for displaying that capacity. It is thus of importance for cognitive neuroscience to know how computationally complex intentional communication actually is. Though the subject of considerable debate, the computational complexity of communication remains so far unknown. In this paper we defend the position that the computational complexity of communication is not a constant, as some views of communication seem to hold, but rather a function of situational factors. We present a methodology for studying and characterizing the computational complexity of communication under different situational constraints. We illustrate our methodology for a model of the problems solved by receivers and senders during a communicative exchange. This approach opens the way to a principled identification of putative model parameters that control cognitive processes supporting intentional communication.

What Does (and Doesn’t) Make Analogical Problem Solving Easy? A Complexity-Theoretic Perspective

Maximum likelihood (ML) (Felsenstein, 1981) is an increasingly popular optimality criterion for selecting evolutionary trees. Finding optimal ML trees appears to be a very hard computational task – in particular, algorithms and heuristics for ML take longer to run than algorithms and heuristics for maximum parsimony (MP). However, while MP has been known to be NP-complete for over 20 years, no such hardness result has been obtained so far for ML.

The parameterized complexity of enumerating frequent itemsets

This paper discusses a new, open-source software program, called Phon, that is designed for the transcription, coding, and analysis of phonological corpora. Phon provides support for multimedia data linkage, segmentation, multiple-blind transcription, transcription validation, syllabification, alignment of target and actual forms, and data analysis. All of these functions are available through a user-friendly graphical interface. Phon, available on most computer platforms, supports data exchange among researchers with the TalkBank XML document format and the Unicode character set. This program provides the basis for the elaboration of PhonBank, a database project that seeks to broaden the scope of CHILDES into phonological development and disorders.