Trace Languages Research Articles

Tracing womyn-born-womyn & trans-exclusion: Into the Michigan Womyn’s Music Festival archive

Few events evoke a divisive response amongst lesbians like the mentioning of the Michigan Womyn’s Music Festival. Autoethnographies, interviews, podcasts, and books – just to name a few – continue to be crafted even after the forty-year festival’s end. Unlike previous publications, this article approaches the festival using archival materials housed at Michigan State University donated by producer, Lisa Vogel, to unpack the signaling rhetoric of womyn-born-womyn (WBW). I center the experience Nancy Burkholder, a transsexual woman expelled from the festival, to navigate, as Nancy tried to navigate, the WBW “policy.” I then take readers on a journey into the archive and articulate my research through calculated steps of tracing language through years of the festival. This article demonstrates how documents, created by festival producers, incited confusion for Nancy Burkholder during the festival and how these same documents now sustain an archival ambiguity.

Tracing language teacher professional development through Perezhivanie: an argument for praxis

ABSTRACT In this paper, we build an argument for studying and promoting teacher development in dialectical teacher-researcher partnership, praxis, which is informed by perezhivanie, a dialectical unity of emotion and intellect . We will study the developmental trajectory of an in-service L2 teacher striving to give her learners agency in the teaching-learning process while navigating institutional structures. We guide the reader through this teacher’s development in a year-and-a-half praxis with two researchers, illustrating the joint process of sense-making to resolve tensions stemming from institutional constraints, learner expectations, and own practices. The data come from (a) teacher-researcher discussions, (b) a teacher interview, and (c) data sessions. Perezhivanie informed the design, researchers’ mediation, and data analysis. We illustrate how the teacher moved towards and realised her commitment to enabling learner agency in language teaching. We discuss the implications of making perezhivanie a central concept in teacher education with in-service L2 teachers, realised through praxis.

Hierarchical structure in language and action: A formal comparison.

Since the cognitive revolution, language and action have been compared as cognitive systems, with cross-domain convergent views recently gaining renewed interest in biology, neuroscience, and cognitive science. Language and action are both combinatorial systems whose mode of combination has been argued to be hierarchical, combining elements into constituents of increasingly larger size. This structural similarity has led to the suggestion that they rely on shared cognitive and neural resources. In this article, we compare the conceptual and formal properties of hierarchy in language and action using set theory. We show that the strong compositionality of language requires a particular formalism, a magma, to describe the algebraic structure corresponding to the set of hierarchical structures underlying sentences. When this formalism is applied to actions, it appears to be both too strong and too weak. To overcome these limitations, which are related to the weak compositionality and sequential nature of action structures, we formalize the algebraic structure corresponding to the set of actions as a trace monoid. We aim to capture the different system properties of language and action in terms of the distinction between hierarchical sets and hierarchical sequences and discuss the implications for the way both systems could be represented in the brain. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Realizable cycle structures in digraphs

Simple cycles on a digraph form a trace monoid under the rule that two such cycles commute if and only if they are vertex disjoint. This rule describes the spatial configuration of simple cycles on the digraph. Cartier and Foata have showed that all combinatorial properties of closed walks are dictated by this trace monoid. We find that most graph properties can be lost while maintaining the monoidal structure of simple cycles and thus cannot be inferred from it, including vertex-transitivity, regularity, planarity, Hamiltonicity, graph spectra, degree distribution and more. Conversely we find that even allowing for multidigraphs, many configurations of simple cycles are not possible at all. The problem of determining whether a given configuration of simple cycles is realizable is highly non-trivial. We show at least that it is decidable and equivalent to the existence of integer solutions to systems of polynomial equations.

A Myhill-Nerode theorem for register automata and symbolic trace languages

We propose a new symbolic trace semantics for register automata (extended finite state machines) which records both the sequence of input symbols that occur during a run as well as the constraints on input parameters that are imposed by this run. Our main result is a generalization of the classical Myhill-Nerode theorem to this symbolic setting. Our generalization requires the use of three relations to capture the additional structure of register automata. Location equivalence ≡l captures that symbolic traces end in the same location, transition equivalence ≡t captures that they share the same final transition, and a partial equivalence relation ≡r captures that symbolic values v and v′ are stored in the same register after symbolic traces w and w′, respectively. A symbolic language is defined to be regular if relations ≡l, ≡t and ≡r exist that satisfy certain conditions, in particular, they all have finite index. We show that the symbolic language associated to a register automaton is regular, and we construct, for each regular symbolic language, a register automaton that accepts this language. Our result provides a foundation for grey-box learning algorithms in settings where the constraints on data parameters can be extracted from code using e.g. tools for symbolic/concolic execution or tainting. Moving to a grey-box setting may overcome the scalability problems of state-of-the-art black-box learning algorithms.

Weak equivalence of higher-dimensional automata

This paper introduces a notion of equivalence for higher-dimensional automata, called weak equivalence. Weak equivalence focuses mainly on a traditional trace language and a new homology language, which captures the overall independence structure of an HDA. It is shown that weak equivalence is compatible with both the tensor product and the coproduct of HDAs and that, under certain conditions, HDAs may be reduced to weakly equivalent smaller ones by merging and collapsing cubes.

Linear automata with translucent letters and linear context-free trace languages

Linear automata with translucent letters are studied. These are finite-state acceptors that have two heads that read the input from opposite sides and for which a set of translucent letters is associated with each state. Thus, head 1, which proceeds from left to right, does not necessarily read the first letter of the current tape content, but it skips a prefix that consists of translucent letters only and reads the first letter after that prefix. Analogously, head 2, which proceeds from right to left, does not necessarily read the last letter, but it skips a suffix that consists of translucent letters only and reads the last letter before that. After such a read operation, the head always returns to its corresponding end of the tape. These linear automata with translucent letters are a generalization of the finite-state acceptors with translucent letters that were studied by the authors in B. Nagy and F. Otto [Finite-state acceptors with translucent letters. In BILC 2011, Proc., edited by G. Bel-Enguix, V. Dahl, and A.O. De La Pente, SciTePress, Portugal (2011) 3-13.] It is shown that these linear automata are strictly more expressive than the model with a single head, but that they still only accept languages that have a semi-linear Parikh image. On the other hand, we obtain a characterization for the class of linear context-free trace languages in terms of a specific class of linear automata with translucent letters.

Markovian dynamics of concurrent systems

Monoid actions of trace monoids over finite sets are powerful models of concurrent systems---for instance they encompass the class of 1-safe Petri nets. We characterise Markov measures attached to concurrent systems by finitely many parameters with suitable normalisation conditions. These conditions involve polynomials related to the combinatorics of the monoid and of the monoid action. These parameters generalise to concurrent systems the coefficients of the transition matrix of a Markov chain. A natural problem is the existence of the uniform measure for every concurrent system. We prove this existence under an irreducibility condition. The uniform measure of a concurrent system is characterised by a real number, the characteristic root of the action, and a function of pairs of states, the Parry cocyle. A new combinatorial inversion formula allows to identify a polynomial of which the characteristic root is the smallest positive root. Examples based on simple combinatorial tilings are studied.

Tracing Language Movement in Africa

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The Generalized Rank of Trace Languages

Given a partially commutative alphabet and a set of words [Formula: see text], the rank of [Formula: see text] expresses the amount of shuffling required to produce a word belonging to [Formula: see text] from two words whose concatenation belongs to the closure of [Formula: see text] with respect to the partial commutation. In this paper, the notion of rank is generalized from concatenations of two words to an arbitrary fixed number of words. In this way, an infinite sequence of non-negative integers and infinity is assigned to every set of words. It is proved that in the case of alphabets defining free commutative monoids, as well as in the more general case of direct products of free monoids, sequences of ranks of regular sets are exactly non-decreasing sequences that are eventually constant. On the other hand, by uncovering a relationship between rank sequences of regular sets and rational series over the min-plus semiring, it is shown that already for alphabets defining free products of free commutative monoids, rank sequences need not be eventually periodic.

Formal and computational modeling of anticipation mechanisms of resilience in the complex sociotechnical air transport system

With ever-growing numbers of passengers and complexity of the air transport system, it becomes more and more of a challenge to manage the system in an effective, safe, and resilient manner. This is especially evident when disruptions occur. Understanding and improving resilience of the air transport system and its adaptive capacity to disruptions is essential for the system’s uninterrupted successful performance. Using theoretical findings from behavioral sciences, this paper makes the first steps towards formalization of the adaptive capacity of resilience of the air transport system with a particular focus on its ability to anticipate. To this end, an expressive logic-based language called Temporal Trace Language is used. The proposed approach is illustrated by a case study, in which anticipatory mechanisms are implemented in an agent-based airport terminal operations model, to deal with a disruptive scenario of unplanned and challenging passenger demand at the security checkpoint. Results showed that the timing of an adaptive action could have a significant influence on reducing the risk of saturation of the system, where saturation implies performance loss. Additionally, trade-off relations were obtained between cost, corresponding to the extra resources mobilized, and the benefits, such as a decrease in risk of saturation of the passenger queue.

Unfolding of Finite Concurrent Automata

We consider recognizable trace rewriting systems with level-regular contexts (RTL). A trace language is level-regular if the set of Foata normal forms of its elements is regular. We prove that the rewriting graph of a RTL is word-automatic. Thus its first-order theory is decidable. Then, we prove that the concurrent unfolding of a finite concurrent automaton with the reachability relation is a RTL graph. It follows that the first-order theory with the reachability predicate (FO[Reach] theory) of such an unfolding is decidable. It is known that this property holds also for the ground term rewriting graphs. We provide examples of finite concurrent automata of which the concurrent unfoldings fail to be ground term rewriting graphs. The infinite grid tree (for each vertex of an infinite grid, there is an edge from this vertex to the origin of a copy of the infinite grid) is such an unfolding. We prove that the infinite grid tree is not a ground term rewriting graph. We have thus obtained a new class of graphs for with a decidable FO[Reach] theory.

The inclusion structure of partially lossy queue monoids and their trace submonoids

We model the behavior of a lossy fifo-queue as a monoid of transformations that are induced by sequences of writing and reading. To have a common model for reliable and lossy queues, we split the alphabet of the queue into two parts: the forgettable letters and the letters that are transmitted reliably. We describe this monoid by means of a confluent and terminating semi-Thue system and then study some of the monoid’s algebraic properties. In particular, we characterize completely when one such monoid can be embedded into another as well as which trace monoids occur as submonoids. Surprisingly, these are precisely those trace monoids that embed into the direct product of two free monoids – which gives a partial answer to a question raised by Diekert et al. at STACS 1995.

Evolutionary dynamics of language systems

Understanding how and why language subsystems differ in their evolutionary dynamics is a fundamental question for historical and comparative linguistics. One key dynamic is the rate of language change. While it is commonly thought that the rapid rate of change hampers the reconstruction of deep language relationships beyond 6,000-10,000 y, there are suggestions that grammatical structures might retain more signal over time than other subsystems, such as basic vocabulary. In this study, we use a Dirichlet process mixture model to infer the rates of change in lexical and grammatical data from 81 Austronesian languages. We show that, on average, most grammatical features actually change faster than items of basic vocabulary. The grammatical data show less schismogenesis, higher rates of homoplasy, and more bursts of contact-induced change than the basic vocabulary data. However, there is a core of grammatical and lexical features that are highly stable. These findings suggest that different subsystems of language have differing dynamics and that careful, nuanced models of language change will be needed to extract deeper signal from the noise of parallel evolution, areal readaptation, and contact.

Control-flow recovery from partial failure reports

Debugging is difficult. When software fails in production, debugging is even harder, as failure reports usually provide only an incomplete picture of the failing execution. We present a system that answers control-flow queries posed by developers as formal languages, indicating whether the query expresses control flow that is possible or impossible for a given failure report. We consider three separate approaches that trade off precision, expressiveness for failure constraints, and scalability. We also introduce a new subclass of regular languages, the unreliable trace languages, which are particularly suited to answering control-flow queries in polynomial time. Our system answers queries remarkably efficiently when we encode failure constraints and user queries entirely as unreliable trace languages.

Classifying recognizable infinitary trace languages using word automata

We address the problem of providing a Borel-like classification of languages of infinite Mazurkiewicz traces, and provide a solution in the framework of ω-automata over infinite words – which is invoked via the sets of linearizations of infinitary trace languages. We identify trace languages whose linearizations are recognized by deterministic weak or deterministic Büchi (word) automata. We present a characterization of the class of linearizations of all recognizable ω-trace languages in terms of Muller (word) automata. Finally, we show that the linearization of any recognizable ω-trace language can be expressed as a Boolean combination of languages recognized by our class of deterministic Büchi automata.

Algebraic Combinatorics on Trace Monoids: Extending Number Theory to Walks on Graphs

Partially commutative monoids provide a powerful tool to study graphs, viewingwalks as words whose letters, the edges of the graph, obey a specific commutation rule. A particularclass of traces emerges from this framework, the hikes, whose alphabet is the set of simple cycleson the graph. We show that hikes characterize undirected graphs uniquely, up to isomorphism, andsatisfy remarkable algebraic properties such as the existence and uniqueness of a prime factorization.Because of this, the set of hikes partially ordered by divisibility hosts a plethora of relations in directcorrespondence with those found in number theory. Some applications of these results are presented,including a permanantal extension to MacMahon's master theorem and a derivation of the Ihara zetafunction.

Changing the idea of language: Nigel Love's perspective

From Nigel Love's perspective, language is a multi-scalar process that connects people, history and nature. In leaving behind the Saussurian tradition's object based views, he contrasts first and second order language. However, the ‘orders’ do not explain each other and, implicated as they are in change, cannot be defined. Indeed, Love suggests that language can describe everything under the sun – except language.I concur that how people speak cannot explain language and, conversely, that linguistic analysis cannot explain how people speak. By tracing language to interdependency between two ‘orders’, Love makes use of carefully crafted tautologies. Such a perspective illustrates the kind of abduction that Gregory Bateson finds across nature. In showing this, I compare how contingency-driven change serves birds with Love's use of beguiling tautologies. These, I claim, contribute much to the productivity of his perspective. While integrationists celebrate his tautologies as paradoxes, in dialogism, there is a tendency to relate them to theses. Others make unexpected changes: the Distributed Language Approach traces language to interactivity between ecological beings and, echoing hylomorphism, others trance human plasticity to the interplay of language, nature and peculiar kind of social agency. As the effects of Love's perspective ripple across the human sciences, I conclude, they are changing the idea of language.

Formal Analysis of an Agent Support Model for Behaviour Change Intervention

Agent applications have been widely used in behaviour change intervention nowadays. This is due to the four features of agents: proactive, reactivity, social ability and autonomy. However, psychological reactance is one of the major limiting causes of agent interventions. Although, many studies have investigated into both psychological reactance and behaviour change nevertheless how reactive intervention can be supported to obtain an improved behaviour change intervention is still lacking in most previous studies. Therefore, this paper describes the formal analysis of agent support model for behaviour change intervention. The analysis made use of two widely accepted approaches in agent formal evaluation namely mathematical analysis and automated verification. The mathematical analysis examined the correctness of the formal model representation and formalization that aimed to ensure that all syntax and semantic representations used in the formal model is consistent. The mathematical analysis used equilibrium property to explore the formal model consistency. Likewise, automated verification depicts the checking of the model properties against its specifications and theoretical traces. The automated verification used Temporal Trace Language (TTL), which verifies the model properties and states against generated traces. The paper presents an agent support model that allows building agent-based software and applications that deflect psychological reactance and enhance an improved behavioural change intervention.

On trace languages generated by (small) spiking neural P systems

We extend to spiking neural P systems a notion investigated in the “standard” membrane systems: the language of the traces of a distinguished object. In our case, we distinguish a spike by “marking” it and we follow its path through the neurons of the system, thus obtaining a language. Several examples are discussed and some preliminary results about this way of associating a language with a spiking neural P system are given, together with a series of topics for further research. For instance, we show that each regular language is the morphic image of a trace language intersected with a very particular regular language, while each recursively enumerable language over the one-letter alphabet is the projection of a trace language.In all proofs we try to keep the size of used systems (number of neurons, of rules in each neuron, of spikes consumed or removed by rules) as small as possible.