Short-circuit evaluation denotes the semantics of propositional connectives in which the second argument is evaluated only if the first argument does not suffice to determine the value of the expression. Free short-ci...
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Dynamic logic combines logic with programs, which at a certain level of abstraction, can be regarded as behaviours changing the system state and, therefore, the truth value of formulas. This paper suggests a method fo...
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ISBN:
(纸本)9780735412873
Dynamic logic combines logic with programs, which at a certain level of abstraction, can be regarded as behaviours changing the system state and, therefore, the truth value of formulas. This paper suggests a method for generating such logics for the domain of robot controllers and illustrates it with a logic for handling resource consumption.
We study the existence of infinite cliques in omega-automatic (hyper-) graphs. It turns out that the situation is much nicer than in general uncountable graphs, but not as nice as for automatic graphs. More specifical...
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ISBN:
(纸本)9783939897163
We study the existence of infinite cliques in omega-automatic (hyper-) graphs. It turns out that the situation is much nicer than in general uncountable graphs, but not as nice as for automatic graphs. More specifically, we show that every uncountable omega-automatic graph contains an un countable co-context-free clique or anticlique, but not necessarily a context-free (let alone regular) clique or anticlique. We also show that uncountable omega-automatic ternary hyper graphs need not have uncountable cliques or anticliques at all.
In the context of the stream calculus, we present an Implicit Function Theorem (IFT) for polynomial systems, and discuss its relations with the classical IFT from calculus. In particular, we demonstrate the advantages...
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In the context of the stream calculus, we present an Implicit Function Theorem (IFT) for polynomial systems, and discuss its relations with the classical IFT from calculus. In particular, we demonstrate the advantages of the stream IFT from a computational point of view, and provide a few example applications where its use turns out to be valuable.
It is known that Metric Temporal logic (MTL) is strictly less expressive than the Monadic First-Order logic of Order and Metric (FO[<;+1]) when interpreted over timed words;this remains true even when the time doma...
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It is known that Metric Temporal logic (MTL) is strictly less expressive than the Monadic First-Order logic of Order and Metric (FO[<;+1]) when interpreted over timed words;this remains true even when the time domain is bounded a priori. In this work, we present an extension of MTL with the same expressive power as FO[<;+1] over bounded timed words (and also, trivially, over time-bounded signals). We then show that expressive completeness also holds in the general (time-unbounded) case if we allow the use of rational constants q is an element of Q in formulas. This extended version of MTL therefore yields a definitive real-time analogue of Kamp's theorem. As an application, we propose a trace-length independent monitoring procedure for our extension of MTL, the first such procedure in a dense real-time setting.
We study the expressiveness and succinctness of history-deterministic pushdown automata (HD-PDA) over finite words, that is, pushdown automata whose nondeterminism can be resolved based on the run constructed so far, ...
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We study the expressiveness and succinctness of history-deterministic pushdown automata (HD-PDA) over finite words, that is, pushdown automata whose nondeterminism can be resolved based on the run constructed so far, but independently of the remainder of the input word. These are also known as good-for-games pushdown *** prove that HD-PDA recognise more languages than deterministic PDA (DPDA) but not all context-free languages (CFL). This class is orthogonal to unambiguous CFL. We further show that HD-PDA can be exponentially more succinct than DPDA, while PDA can be double-exponentially more succinct than HD-PDA. We also study HDness in visibly pushdown automata (VPA), which enjoy better closure properties than PDA, and for which we show that deciding HDness is ExPTimE-complete. HD-VPA can be exponentially more succinct than deterministic VPA, while VPA can be exponentially more succinct than HD-VPA. Both of these lower bounds are *** then compare HD-PDA with PDA for which composition with games is well-behaved, i.e. good-for-games automata. We show that these two notions coincide, but only if we consider potentially infinitely branching ***, we study the complexity of resolving nondeterminism in HD-PDA. Every HDPDA has a positional resolver, a function that resolves nondeterminism and that is only dependent on the current configuration. Pushdown transducers are sufficient to implement the resolvers of HD-VPA, but not those of HD-PDA. HD-PDA with finite-state resolvers are determinisable.
A linear inference is a valid inequality of Boolean algebra in which each variable occurs at most once on each side. In this work we leverage recently developed graphical representations of linear formulae to build an...
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A linear inference is a valid inequality of Boolean algebra in which each variable occurs at most once on each side. In this work we leverage recently developed graphical representations of linear formulae to build an implementation that is capable of more efficiently searching for switch-medial -independent inferences. We use it to find four 'minimal' 8-variable independent inferences and also prove that no smaller ones exist;in contrast, a previous approach based directly on formulae reached computational limits already at 7 variables. Two of these new inferences derive some previously found independent linear inferences. The other two (which are dual) exhibit structure seemingly beyond the scope of previous approaches we are aware of;in particular, their existence contradicts a conjecture of Das and Strassburger. We were also able to identify 10 minimal 9-variable linear inferences independent of all the aforementioned inferences, comprising 5 dual pairs, and present applications of our implementation to recent 'graph logics'.
The TTE approach to Computable Analysis is the study of so-called representations (encodings for continuous objects such as reals, functions, and sets) with respect to the notions of computability they induce. A rich ...
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The TTE approach to Computable Analysis is the study of so-called representations (encodings for continuous objects such as reals, functions, and sets) with respect to the notions of computability they induce. A rich variety of such representations had been devised over the past decades, particularly regarding closed subsets of Euclidean space plus subclasses thereof (like compact subsets). In addition, they had been compared and classified with respect to both non-uniform computability of single sets and uniform computability of operators on sets. In this paper we refine these investigations from the point of view of computational complexity. Benefiting from the concept of second-order representations and complexity recently devised by Kawamura & Cook (2012), we determine parameterized complexity bounds for operators such as union, intersection, projection, and more generally function image and inversion. By indicating natural parameters in addition to the output precision, we get a uniform view on results by Ko (1991-2013), Braverman (2004/05) and Zhao & Muller (2008), relating these problems to the P/UP/NP question in discrete complexity theory.
作者：
Finkel, OlivierCNRS
Inst Math Jussieu Paris Rive Gauche Equipe Logique Math F-75700 Paris France Univ Paris 07
F-75221 Paris 05 France
An omega-language is a set of infinite words over a finite alphabet X. We consider the class of recursive omega-languages, i.e. the class of omega-languages accepted by Turing machines with a Buchi acceptance conditio...
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An omega-language is a set of infinite words over a finite alphabet X. We consider the class of recursive omega-languages, i.e. the class of omega-languages accepted by Turing machines with a Buchi acceptance condition, which is also the class Sigma(1)(1) of (effective) analytic subsets of X-omega for some finite alphabet X. We investigate here the notion of ambiguity for recursive omega-languages with regard to acceptance by Buchi Turing machines. We first present in detail essentials on the literature on omega-languages accepted by Turing Machines. Then we give a complete and broad view on the notion of ambiguity and unambiguity of Buchi Turing machines and of the omega-languages they accept. To obtain our new results, we make use of results and methods of effective descriptive set theory.
The author has recently introduced an abstract algebraic framework of analogical proportions within the general setting of universal algebra. This paper studies analogical proportions in the boolean domain consisting ...
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The author has recently introduced an abstract algebraic framework of analogical proportions within the general setting of universal algebra. This paper studies analogical proportions in the boolean domain consisting of two elements 0 and 1 within his framework. It turns out that our notion of boolean proportions coincides with two prominent models from the literature in different settings. This means that we can capture two separate modellings of boolean proportions within a single framework which is mathematically appealing and provides further evidence for the robustness and applicability of the general framework.
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