Advances and applications of automata on words and trees : executive summary

Seminar: 10501 - Advances and Applications of Automata on Words and Trees. The aim of the seminar was to discuss and systematize the recent fast progress in automata theory and to identify important directions for future research. For this, the seminar brought together more than 40 researchers from automata theory and related fields of applications. We had 19 talks of 30 minutes and 5 one-hour lectures leaving ample room for discussions. In the following we describe the topics in more detail

Words by convention

Existing metasemantic projects presuppose that word- (or sentence-) types are part of the non-semantic base. We propose a new strategy: an endogenous account of word types, that is, one where word types are fixed as part of the metasemantics. On this view, it is the conventions of truthfulness and trust that ground not only the meaning of the words (meaning by convention) but also what the word type is of each particular token utterance (words by convention). The same treatment extends to identifying the populations through which the conventions prevail. We consider whether this proposal leads to new underdetermination challenges for metasemantics, and make a case that it does not

On the Commutative Equivalence of Context-Free Languages

The problem of the commutative equivalence of context-free and regular languages is studied. In particular conditions ensuring that a context-free language of exponential growth is commutatively equivalent with a regular language are investigated

Deciding regular grammar logics with converse through first-order logic

We provide a simple translation of the satisfiability problem for regular grammar logics with converse into GF2, which is the intersection of the guarded fragment and the 2-variable fragment of first-order logic. This translation is theoretically interesting because it translates modal logics with certain frame conditions into first-order logic, without explicitly expressing the frame conditions. A consequence of the translation is that the general satisfiability problem for regular grammar logics with converse is in EXPTIME. This extends a previous result of the first author for grammar logics without converse. Using the same method, we show how some other modal logics can be naturally translated into GF2, including nominal tense logics and intuitionistic logic. In our view, the results in this paper show that the natural first-order fragment corresponding to regular grammar logics is simply GF2 without extra machinery such as fixed point-operators.Comment: 34 page

Complex systems and the history of the English language

Complexity theory (Mitchell 2009, Kretzschmar 2009) is something that historical linguists not only can use but should use in order to improve the relationship between the speech we observe in historical settings and the generalizations we make from it. Complex systems, as described in physics, ecology, and many other sciences, are made up of massive numbers of components interacting with one another, and this results in self-organization and emergent order. For speech, the “components” of a complex system are all of the possible variant realizations of linguistic features as they are deployed by human agents, speakers and writers. The order that emerges in speech is simply the fact that our use of words and other linguistic features is significantly clustered in the spatial and social and textual groups in which we actually communicate. Order emerges from such systems by means of self-organization, but the order that arises from speech is not the same as what linguists study under the rubric of linguistic structure. In both texts and regional/social groups, the frequency distribution of features occurs as the same pattern: an asymptotic hyperbolic curve (or “A-curve”). Formal linguistic systems, grammars, are thus not the direct result of the complex system, and historical linguists must use complexity to mediate between the language production observed in the community and the grammars we describe. The history of the English language does not proceed as regularly as like clockwork, and an understanding of complex systems helps us to see why and how, and suggests what we can do about it. First, the scaling property of complex systems tells us that there are no representative speakers, and so our observation of any small group of speakers is unlikely to represent any group at a larger scale—and limited evidence is the necessary condition of many of our historical studies. The fact that underlying complex distributions follow the 80/20 rule, i.e. 80% of the word tokens in a data set will be instances of only 20% of the word types, while the other 80% of the word types will amount to only 20% of the tokens, gives us an effective tool for estimating the status of historical states of the language. Such a frequency-based technique is opposed to the typological “fit” technique that relies on a few texts that can be reliably located in space, and which may not account for the crosscutting effects of text type, another dimension in which the 80/20 rule applies. Besides issues of sampling, the frequency-based approach also affects how we can think about change. The A-curve immediately translates to the S-curve now used to describe linguistic change, and explains that “change” cannot reasonably be considered to be a qualitative shift. Instead, we can use to model of “punctuated equilibrium” from evolutionary biology (e.g., see Gould and Eldredge 1993), which suggests that multiple changes occur simultaneously and compete rather than the older idea of “phyletic gradualism” in evolution that corresponds to the traditional method of historical linguistics. The Great Vowel Shift, for example, is a useful overall generalization, but complex systems and punctuated equilibrium explain why we should not expect it ever to be “complete” or to appear in the same form in different places. These applications of complexity can help us to understand and interpret our existing studies better, and suggest how new studies in the history of the English language can be made more valid and reliable

On the Degree of Extension of Some Models Defining Non-Regular Languages

This work is a survey of the main results reported for the degree of extension of two models defining non-regular languages, namely the context-free grammar and the extended automaton over groups. More precisely, we recall the main results regarding the degree on non-regularity of a context-free grammar as well as the degree of extension of finite automata over groups. Finally, we consider a similar measure for the finite automata with translucent letters and present some preliminary results. This measure could be considered for many mechanisms that extend a less expressive one.Comment: In Proceedings AFL 2023, arXiv:2309.0112