1,720,997 research outputs found
A Coalgebraic Decision Procedure for WS1S
Full text linkWeak monadic second-order logic of one successor (WS1S) is a simple and natural formalism to specify regular properties. WS1S is decidable, although the decision procedure's complexity is non-elementary. Typically, decision procedures for WS1S exploit the logic-automaton connection, i.e. they escape the simple and natural formalism by translating formulas into equally expressive regular structures such as finite automata, regular expressions, or games. In this work, we devise a coalgebraic decision procedure for WS1S that stays within the logical world by directly operating on formulas. The key operation is the derivative of a formula, modeled after Brzozowski's derivatives of regular expressions. The presented decision procedure has been formalized and proved correct in the interactive proof assistant Isabelle
Formal Languages, Formally and Coinductively
Full text linkTraditionally, formal languages are defined as sets of words. More
recently, the alternative coalgebraic or coinductive representation as
infinite tries, i.e., prefix trees branching over the alphabet, has
been used to obtain compact and elegant proofs of classic results in
language theory. In this paper, we study this representation in the
Isabelle proof assistant. We define regular operations on infinite
tries and prove the axioms of Kleene algebra for those
operations. Thereby, we exercise corecursion and coinduction and
confirm the coinductive view being profitable in formalizations, as it
improves over the set-of-words view with respect to proof automation
Quotients of Bounded Natural Functors
Full text linkThe functorial structure of type constructors is the foundation for many definition and proof principles in higher-order logic (HOL). For example, inductive and coinductive datatypes can be built modularly from bounded natural functors (BNFs), a class of well-behaved type constructors. Composition, fixpoints, and—under certain conditions—subtypes are known to preserve the BNF structure. In this article, we tackle the preservation question for quotients, the last important principle for introducing new types in HOL. We identify sufficient conditions under which a quotient inherits the BNF structure from its underlying type. Surprisingly, lifting the structure in the obvious manner fails for some quotients, a problem that also affects the quotients of polynomial functors used in the Lean proof assistant. We provide a strictly more general lifting scheme that supports such problematic quotients. We extend the Isabelle/HOL proof assistant with a command that automates the registration of a quotient type as a BNF, reducing the proof burden on the user from the full set of BNF axioms to our inheritance conditions. We demonstrate the command’s usefulness through several case studies.</p
Efficient Evaluation of Arbitrary Relational Calculus Queries
Full text linkThe relational calculus (RC) is a concise, declarative query language.
However, existing RC query evaluation approaches are inefficient and often
deviate from established algorithms based on finite tables used in database
management systems. We devise a new translation of an arbitrary RC query into
two safe-range queries, for which the finiteness of the query's evaluation
result is guaranteed. Assuming an infinite domain, the two queries have the
following meaning: The first is closed and characterizes the original query's
relative safety, i.e., whether given a fixed database, the original query
evaluates to a finite relation. The second safe-range query is equivalent to
the original query, if the latter is relatively safe. We compose our
translation with other, more standard ones to ultimately obtain two SQL
queries. This allows us to use standard database management systems to evaluate
arbitrary RC queries. We show that our translation improves the time complexity
over existing approaches, which we also empirically confirm in both realistic
and synthetic experiments
Automated reasoning for explainable artificial intelligence
Full text linkReasoning and learning have been considered fundamental features of intelligence ever since the dawn of the field of artificial intelligence, leading to the development of the research areas of automated reasoning and machine learning. This short paper is a non-technical position statement that aims at prompting a discussion of the relationship between automated reasoning and machine learning, and more generally between automated reasoning and artificial intelligence. We suggest that the emergence of the new paradigm of XAI, that stands for eXplainable Artificial Intelligence, is an opportunity for rethinking these relationships, and that XAI may offer a grand challenge for future research on automated reasoning
Generic Authenticated Data Structures, Formally
Full text linkAuthenticated data structures are a technique for outsourcing data storage and maintenance to an untrusted server. The server is required to produce an efficiently checkable and cryptographically secure proof that it carried out precisely the requested computation. Recently, Miller et al. [https://doi.org/10.1145/2535838.2535851] demonstrated how to support a wide range of such data structures by integrating an authentication construct as a first class citizen in a functional programming language. In this paper, we put this work to the test of formalization in the Isabelle proof assistant. With Isabelle’s help, we uncover and repair several mistakes and modify the small-step semantics to perform call-by-value evaluation rather than requiring terms to be in administrative normal form
From Nondeterministic to Multi-Head Deterministic Finite-State Transducers (Track B: Automata, Logic, Semantics, and Theory of Programming)
Full text linkEvery nondeterministic finite-state automaton is equivalent to a deterministic finite-state automaton. This result does not extend to finite-state transducers - finite-state automata equipped with a one-way output tape. There is a strict hierarchy of functions accepted by one-way deterministic finite-state transducers (1DFTs), one-way nondeterministic finite-state transducers (1NFTs), and two-way nondeterministic finite-state transducers (2NFTs), whereas the two-way deterministic finite-state transducers (2DFTs) accept the same family of functions as their nondeterministic counterparts (2NFTs).
We define multi-head one-way deterministic finite-state transducers (mh-1DFTs) as a natural extension of 1DFTs. These transducers have multiple one-way reading heads that move asynchronously over the input word. Our main result is that mh-1DFTs can deterministically express any function defined by a one-way nondeterministic finite-state transducer. Of independent interest, we formulate the all-suffix regular matching problem, which is the problem of deciding for each suffix of an input word whether it belongs to a regular language. As part of our proof, we show that an mh-1DFT can solve all-suffix regular matching, which has applications, e.g., in runtime verification
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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