Don't care words with an application totheautomata-based approach for real addition

Automata have proved to be a useful tool in infinite-state model checking, since they can represent infinite sets of integers and reals. However, analogous to the use of binary decision diagrams (bdds) to represent finite sets, the sizes of the automata are an obstacle in the automata-based set representation. In this article, we generalize the notion of "don't cares” for bdds to word languages as a means to reduce the automata sizes. We show that the minimal weak deterministic Büchi automaton (wdba) with respect to a given don't care set, under certain restrictions, is uniquely determined and can be efficiently constructed. We apply don't cares to improve the efficiency of a decision procedure for the first-order logic over the mixed linear arithmetic over the integers and the reals based on wdba

The systematic guideline review: method, rationale, and test on chronic heart failure

Background: Evidence-based guidelines have the potential to improve healthcare. However, their de-novo-development requires substantial resources-especially for complex conditions, and adaptation may be biased by contextually influenced recommendations in source guidelines. In this paper we describe a new approach to guideline development-the systematic guideline review method (SGR), and its application in the development of an evidence-based guideline for family physicians on chronic heart failure (CHF). Methods: A systematic search for guidelines was carried out. Evidence-based guidelines on CHF management in adults in ambulatory care published in English or German between the years 2000 and 2004 were included. Guidelines on acute or right heart failure were excluded. Eligibility was assessed by two reviewers, methodological quality of selected guidelines was appraised using the AGREE instrument, and a framework of relevant clinical questions for diagnostics and treatment was derived. Data were extracted into evidence tables, systematically compared by means of a consistency analysis and synthesized in a preliminary draft. Most relevant primary sources were re-assessed to verify the cited evidence. Evidence and recommendations were summarized in a draft guideline. Results: Of 16 included guidelines five were of good quality. A total of 35 recommendations were systematically compared: 25/35 were consistent, 9/35 inconsistent, and 1/35 un-rateable (derived from a single guideline). Of the 25 consistencies, 14 were based on consensus, seven on evidence and four differed in grading. Major inconsistencies were found in 3/9 of the inconsistent recommendations. We re-evaluated the evidence for 17 recommendations (evidence-based, differing evidence levels and minor inconsistencies) - the majority was congruent. Incongruity was found where the stated evidence could not be verified in the cited primary sources, or where the evaluation in the source guidelines focused on treatment benefits and underestimated the risks. The draft guideline was completed in 8.5 man-months. The main limitation to this study was the lack of a second reviewer. Conclusion: The systematic guideline review including framework development, consistency analysis and validation is an effective, valid, and resource saving-approach to the development of evidence-based guidelines

Upper bounds on the automata size for integer and mixed real and integer linear arithmetic

Abstract. Automata-based decision procedures have proved to be a particularly useful tool for infinite-state model checking, where automata are used to represent sets of real and integer values. However, not all theoretical aspects of these decision procedures are completely understood. We establish triple exponential upper bounds on the automata size for FO(Z,+, <) and FO(R, Z,+, <). While a similar bound for Presburger Arithmetic, i.e., FO(Z,+, <) was obtained earlier using a quantifier elimination based approach, the bound for FO(R, Z, +,<) is novel. We define two graded back-and-forth systems, and use them to derive bounds on the automata size by establishing a connection between those systems and languages that can be described by formulas in the respective logics. With these upper bounds that match the known lower bounds, the theoretical background for automata-based decision procedures for linear arithmetics becomes more complete.

Don’t care words with an application to the automata-based approach for real addition

ISSN:0925-9856ISSN:1572-810

Mechanizing the powerset construction for restricted classes of ω-automata

Abstract. Automata over infinite words provide a powerful framework to solve various decision problems. However, the mechanized reasoning with restricted classes of automata over infinite words is often simpler and more efficient. For instance, weak deterministic Büchi automata (wdbas) can be handled algorithmically almost as efficient as deterministic automata over finite words. In this paper, we show how and when the standard powerset construction for automata over finite words can be used to determinize automata over infinite words. An instance is the class of automata that accept wdba-recognizable languages. Furthermore, we present applications of this new determinization construction. Namely, we apply it to improve the automata-based approach for the mixed firstorder linear arithmetic over the reals and the integers, and we utilize it to accelerate finite state model checking. We report on experimental results for these two applications.

LIRA: Handling Constraints of Linear Arithmetics over the Integers and the Reals ⋆

The mechanization of many verification tasks relies on efficient implementations of decision procedures for fragments of first-order logic. Interactiv

An Automata-Based Approach.

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