Decidability of bisimulation equivalence for processes generating context-free languages

A context-free grammar (CFG) in Greibach Normal Form coincides, in another notation, with a system of guarded recursion equations in Basic Process Algebra. Hence to each CFG a process can be assigned as solution, which has as its set of finite traces the context-free language (CFL) determined by that CFG. While the equality problem for CFL's is unsolvable, the equality problem for the processes determined by CFG's turns out to be solvable. Here equality on processes is given by a model of process graphs modulo bisimulation equivalence. The proof is given by displaying a periodic structure of the process graphs determined by CFG's. As a corollary of the periodicity a short proof of the solvability of the equivalence problem for simple context-free languages is given

Decidability of bisimulation equivalence for processes generating context-free languages

A context-free grammar (CFG) in Greibach Normal Form coincides, in another notation, with a system of guarded recursion equations in Basic Process Algebra. Hence to each CFG a process can be assigned as solution, which has as its set of finite traces the context-free language (CFL) determined by that CFG. While the equality problem for CFL's is unsolvable, the equality problem for the processes determined by CFG's turns out to be solvable. Here equality on processes is given by a model of process graphs modulo bisimulation equivalence. The proof is given by displaying a periodic structure of the process graphs determined by CFG's. As a corollary of the periodicity a short proof of the solvability of the equivalence problem for simple context-free languages is given

Evaluating the role of quantitative modeling in language evolution

Models are a flourishing and indispensable area of research in language evolution. Here we highlight critical issues in using and interpreting models, and suggest viable approaches. First, contrasting models can explain the same data and similar modelling techniques can lead to diverging conclusions. This should act as a reminder to use the extreme malleability of modelling parsimoniously when interpreting results. Second, quantitative techniques similar to those used in modelling language evolution have proven themselves inadequate in other disciplines. Cross-disciplinary fertilization is crucial to avoid mistakes which have previously occurred in other areas. Finally, experimental validation is necessary both to sharpen models' hypotheses, and to support their conclusions. Our belief is that models should be interpreted as quantitative demonstrations of logical possibilities, rather than as direct sources of evidence. Only an integration of theoretical principles, quantitative proofs and empirical validation can allow research in the evolution of language to progress

From holism to compositionality: memes and the evolution of segmentation, syntax, and signification in music and language

Steven Mithen argues that language evolved from an antecedent he terms “Hmmmmm, [meaning it was] Holistic, manipulative, multi-modal, musical and mimetic”. Owing to certain innate and learned factors, a capacity for segmentation and cross-stream mapping in early Homo sapiens broke the continuous line of Hmmmmm, creating discrete replicated units which, with the initial support of Hmmmmm, eventually became the semantically freighted words of modern language. That which remained after what was a bifurcation of Hmmmmm arguably survived as music, existing as a sound stream segmented into discrete units, although one without the explicit and relatively fixed semantic content of language. All three types of utterance – the parent Hmmmmm, language, and music – are amenable to a memetic interpretation which applies Universal Darwinism to what are understood as language and musical memes. On the basis of Peter Carruthers’ distinction between ‘cognitivism’ and ‘communicativism’ in language, and William Calvin’s theories of cortical information encoding, a framework is hypothesized for the semantic and syntactic associations between, on the one hand, the sonic patterns of language memes (‘lexemes’) and of musical memes (‘musemes’) and, on the other hand, ‘mentalese’ conceptual structures, in Chomsky’s ‘Logical Form’ (LF)