A. AYARI, D. BASIN, AND S. FRIEDRICH, Structural and behavioral modeling with monadic logics, in Proc. 29th International Symposium on Multiple-Valued Logic, ISMVL '99, IEEE Computer Society, May 1999.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....or a transition table. The niche for Mona applications contains those structures that are too large and complicated to describe by other means, yet not so large as to require infeasible computations. Happily, many interesting projects fit into this niche, including hardware verification [4, 1], pointer analysis [22, 16, 38] controller synthesis [44, 21] natural languages [39] parsing tools [13] software design descriptions [28] Presburger arithmetic [45] and verification of concurrent systems [31, 30, 23, 42, 46] There are a number of tools resembling Mona. Independent of the ....

Abdelwaheb Ayari, David Basin, and Stefan Friedrich. Structural and behavioral modeling with monadic logics. In The Twenty-Ninth IEEE International Symposium on Multiple-Valued Logic. IEEE Computer Society, 1999.

.... and the decidability of the weak monadic second order logic of two successors, WS2S, was shown using tree automata [22, 8] Although the theory of WS1S is non elementary decidable [20] the Mona system [16, 9] decision procedures for WS1S and WS2S has proved useful and ecient in practice, e.g. [3, 1, 10]. The decidability result presented here, exploits analogously to the decision procedures for WS1S and WS2S the relation between automata and monadic second order logics. But instead of using word automata that read words and tree automata that read trees, we use tree automata to describe ....

....inductive functions (EIFs) were used to describe parameterized families of combinational tree structured circuits. It is possible to represent EIFs in WS1S since in [2, 18] it was shown that they are equivalent to alternating tree automata restricted on complete leaf labeled trees. In [3, 1] WS1S and WS2S were used to reason about serial and tree structured parameterized circuits. Since the network topology of a tree structured circuit is normally a complete tree where the leaves are the inputs of the circuit, WS1S appears to be more natural than WS2S for modeling tree structured ....

A. Ayari, D. Basin, and S. Friedrich. Structural and behavioral modeling with monadic logics. In 29th IEEE International Symposium on Multiple-Valued Logic, pages 142-151, 1999.

....ideas have led to a whole branch of research. Another kind of application is to reduce other logics to the MONA logics. Hardware verification One of the first MONA applications was hardware verification. In [BK98] the ideas of modeling parameterized systems or discrete time were introduced. In [ABF99] this verification technique is further described and generalized to trees. Many of the applications mentioned below also build on these ideas. Controller synthesis As mentioned, M2L Str can be viewed as a temporal logic, that is, as a logic modeling the occurrence of events over time. In ....

Abdelwaheb Ayari, David Basin, and Stefan Friedrich. Structural and behavioral modeling with monadic logics. In IEEE International Symposium on MultipleValued Logic. IEEE Computer Society, 1999.

....expression or a transition table. The niche for Mona applications contains those structures that are too large and complicated to describe by other means, yet not so large as to require infeasible computations. Happily, many interesting projects t into this niche, including hardware veri cation [4, 1], pointer analysis [23, 17] controller synthesis [44, 22] natural languages [39] parsing tools [14] software design descriptions [29] Presburger arithmetic [45] and veri cation of concurrent systems [32, 31, 24, 42, 46] There are a number of tools resembling Mona. Independently of the Mona ....

Abdelwaheb Ayari, David Basin, and Stefan Friedrich. Structural and behavioral modeling with monadic logics. In The Twenty-Ninth IEEE International Symposium on Multiple-Valued Logic. IEEE Computer Society, 1999.

....adder is built by chaining together (ripple carry fashion) n copies of a full one bit adder, where carries are propagated along an internal line of carries C. The speci cation of the auxiliary formulae full adder, at least two and mod two are straightforward Boolean formulae and can be found in [2]. The equivalence between the speci cation and the implementation of the adder is stated by the formula 8n: 8A; B; S: 8c i ; c o : adder(n; A; B; S; c i ; c o ) 1) spec(n; A; B; S; c i ; c o ) In this example, BMC takes as input the negation of (1) and a natural number k. It produces a ....

Abdelwaheb Ayari, David Basin, and Stefan Friedrich. Structural and behavioral modeling with monadic logics. In Rolf Drechsler and Bernd Becker, editors, The Twenty-Ninth IEEE International Symposium on Multiple-Valued Logic. IEEE Computer Society, Los Alamitos, Freiburg, Germany, May 1999.

....adder is built by chaining together (ripple carry fashion) n copies of a full one bit adder, where carries are propagated along an internal line of carries C. The specification of the auxiliary formulae full adder, at least two and mod two are straightforward Boolean formulae and can be found in [2]. The equivalence between the specification and the implementation of the adder is stated by the formula # #n. #A, B, S. #c i , c o . adder(n, A, B, S, c i , c o ) 1) spec(n, A, B, S, c i , c o ) In this example, BMC takes as input the negation of (1) and a natural number k. It produces ....

Abdelwaheb Ayari, David Basin, and Stefan Friedrich. Structural and behavioral modeling with monadic logics. In Rolf Drechsler and Bernd Becker, editors, The Twenty-Ninth IEEE International Symposium on Multiple-Valued Logic. IEEE Computer Society, Los Alamitos, Freiburg, Germany, May 1999.

....use of BDDs to represent word automata, without alternation, has been explored in [12,15] There, BDD represented automata are used to provide a decision procedure for WS1S. 22 This decision procedure is implemented in the Mona system and also used to formalize and reason about hardware, e.g. [1,2]. WS1S formalize the same class of languages as LIFs, namely regular languages on words. However, this logic is more expressive in the sense that there are regular languages whose representation as automata, and hence also LIFs, are nonelementary larger than the corresponding formulae in WS1S ....

A. Ayari, D. Basin, and S. Friedrich. Structural and behavioral modeling with monadic logics. In IEEE International Symposium on Multiple-Valued Logic, ISMVL'99, pages 142-151, Freiburg, Germany, 1999.

....use of BDDs to represent word automata, without alternation, has been explored in [12,15] There, BDD represented automata are used to provide a decision procedure for WS1S. 22 This decision procedure is implemented in the Mona system and also used to formalize and reason about hardware, e.g. [1,2]. WS1S formalize the same class of languages as LIFs, namely regular languages on words. However, this logic is more expressive in the sense that there are regular languages whose representation as automata, and hence also LIFs, are nonelementary larger than the corresponding formulae in WS1S ....

A. Ayari, D. Basin, and S. Friedrich. Structural and behavioral modeling with monadic logics. In IEEE International Symposium on Multiple-Valued Logic, ISMVL'99, pages 142-151, 1999.

....The use of BDDs to represent word automata, without alternation, has been explored in [12,15] There, BDD represented automata are used to provide a decision procedure for WS1S. This decision procedure is implemented in the Mona system and also used to formalize and reason about hardware, e.g. [1,2]. WS1S formalize the same class of languages as LIFs, namely regular languages on words. However, this logic is more expressive in the sense that there are regular languages whose representation as automata, and hence also LIFs, are nonelementary larger than the corresponding formulae in WS1S ....

A. Ayari, D. Basin, and S. Friedrich. Structural and behavioral modeling with monadic logics. In The Twenty-Ninth IEEE International Symposium on Multiple-Valued Logic, pages 142-151. IEEE Computer Society, 1999.

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A. AYARI, D. BASIN, AND S. FRIEDRICH, Structural and behavioral modeling with monadic logics, in Proc. 29th International Symposium on Multiple-Valued Logic, ISMVL '99, IEEE Computer Society, May 1999.

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