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It is shown that formulas in monadic second order logic (mso) with one free variable can be mimicked by attribute grammars with a designated boolean attribute and vice versa. We prove that mso formulas with two free variables have the same power in defining binary relations on nodes of a tree as regular path languages have. For graphs in general, mso formulas turn out to be stronger. We also compare path languages against the routing languages of Klarlund and Schwartzbach. We compute the complexity of evaluating mso formulas with free variables, especially in the case where there is a dependency between free variables of the formula. Last, it is proven that mso tree transducers have the same strength as attributed tree transducers with the single use requirement and flags.

In this paper we present a formal approach to modelling context effect in perceptual domains: namely how the perception of an object is effected by other objects. Our approach is operational and perceptually motivated in the sense that we focus on how objects are perceived as being constructed from certain components. Based on a psychological theory of perception, called Structural Information Theory, we develop an algebraic model for context sensitive perception. We illustrate our model by using the domain of alphabetic strings and discuss its extension to the domain of visual objects. Finally, we remark on how this approach can be applied to model context effect in non-perceptual situation, and then make some observations on the general problem of context.

In this paper we propose an algebraic method for solving proportional analogy problems involving sequential patterns. In this approach, sequential patterns are considered as elements of an algebra. The gestalt that is assigned to a pattern is represented by the term of the algebra that denotes it. Most patterns are ambiguous: there are different terms that correspond to a pattern, representing different gestalts of it. When a pattern is perceived as part of a proportional analogy, it may assume a different gestalt than when it is viewed in isolation. We consider analogical relations as mappings between algebras and give a formal definition of the preferred gestalts for an analogy in terms of the simplicity of algebraic terms that denote the patterns involved in the proportional analogy. We conjecture that these terms correspond to the gestalts that are perceived by a human who solves the proportional analogy problem. Finally, we describe an algorithm to solve the proportional analogy p...

One of the major unsolved problems in perception is to explain why a sensory pattern, which may in principle be perceived as having different constituent structures (gestalts), is usually perceived as having one particular gestalt. Structural Information Theory (SIT) treats Gestalt perception as disambiguation and describe it by a perceptually motivated preference relation de ned on possible gestalts of patterns. The existing models of SIT ignore the context effects which is essential in determining the gestalt of patterns. We introduce a SIT model and embed it in a framework where two types of context effects are integrated: 1) the effect of simultaneous presence of other patterns, and 2) the effect of the task to be accomplished on the basis of the patterns. In order to illustrate the interaction of these types of context effects with perception, we consider proportional analogy problems defined on strings (alphabetic patterns). Such a proportional analogy problem consists of three simultaneously present strings and the task is to find a fourth string by means of analogical projections on the given strings. To this

presented algebras and groups defined by permutation relations ∗.