Minimizing Deterministic Lattice Automata

Halamish, Shulamit; Kupferman, Orna

doi:10.1007/978-3-642-19805-2_14

Cited by 3 publications

(10 citation statements)

References 18 publications

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“…Specifically, we used the fact that states in such a DFA have separating words. It is known that there is no canonical minimal LDFA for a lattice language [22]. However, we show below that it is possible to assume that the specification is given by means of an LDFA whose states have separating words.…”

Section: Separable Ldfasmentioning

confidence: 91%

“…An exception is the problem of minimization of LDFAs, which is NP-complete [22]. It is shown in [22] that there is no canonical minimal LDFA for a latticed language.…”

Section: Computation-based Costmentioning

confidence: 99%

“…An exception is the problem of minimization of LDFAs, which is NP-complete [22]. It is shown in [22] that there is no canonical minimal LDFA for a latticed language. Recall that minimal DFAs play a key role in our upper bound for the design problem in the closed setting (Theorem 3.1) as we assumed the specification is given as such a DFA.…”

Section: Computation-based Costmentioning

confidence: 99%

“…While the set of possible values that an LDFA assigns is finite, circumventing many of the technical difficulties in general weighted automata, handling box LDFAs involves other technical difficulties. In particular, there is no canonical minimal LDFA for a given language [22]. This is problematic, as minimal DFAs play a key role in our solution to the design problem in the closed setting.…”

Section: Introductionmentioning

confidence: 99%

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Synthesis from Component Libraries with Costs

Avni

Kupferman

2014

CONCUR 2014 – Concurrency Theory

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Synthesis is the automated construction of a system from its specification. In real life, hardware and software systems are rarely constructed from scratch. Rather, a system is typically constructed from a library of components. Lustig and Vardi formalized this intuition and studied LTL synthesis from component libraries. In real life, designers seek optimal systems. In this paper we add optimality considerations to the setting. We distinguish between quality considerations (for example, size -the smaller a system is, the better it is), and pricing (for example, the payment to the company who manufactured the component). We study the problem of designing systems with minimal quality-cost and price. A key point is that while the quality cost is individual -the choices of a designer are independent of choices made by other designers that use the same library, pricing gives rise to a resource-allocation game -designers that use the same component share its price, with the share being proportional to the number of uses (a component can be used several times in a design). We study both closed and open settings, and in both we solve the problem of finding an optimal design. In a setting with multiple designers, we also study the game-theoretic problems of the induced resource-allocation game.

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Section: Separable Ldfasmentioning

confidence: 91%

“…An exception is the problem of minimization of LDFAs, which is NP-complete [22]. It is shown in [22] that there is no canonical minimal LDFA for a latticed language.…”

Section: Computation-based Costmentioning

confidence: 99%

Section: Computation-based Costmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Synthesis from Component Libraries with Costs

Avni

Kupferman

2014

CONCUR 2014 – Concurrency Theory

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“…In [13], we studied the minimization problem for LDFAs. We showed that it is impossible to define a right congruence in the context of latticed languages, and that no canonical minimal LDFA exists.…”

Section: Introductionmentioning

confidence: 99%

Approximating Deterministic Lattice Automata

Halamish

Kupferman

2012

Automated Technology for Verification and Analysis

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Abstract. Traditional automata accept or reject their input, and are therefore Boolean. Lattice automata generalize the traditional setting and map words to values taken from a lattice. In particular, in a fully-ordered lattice, the elements are 0, 1, . . . , n − 1, ordered by the standard ≤ order. Lattice automata, and in particular lattice automata defined with respect to fully-ordered lattices, have interesting theoretical properties as well as applications in formal methods. Minimal deterministic automata capture the combinatorial nature and complexity of a formal language. Deterministic automata have many applications in practice. In [13], we studied minimization of deterministic lattice automata. We proved that the problem is in general NP-complete, yet can be solved in polynomial time in the case the lattices are fully-ordered. The multi-valued setting makes it possible to combine reasoning about lattice automata with approximation. An approximating automaton may map a word to a range of values that are close enough, under some pre-defined distance metric, to its exact value. We study the problem of finding minimal approximating deterministic lattice automata defined with respect to fully-ordered lattices. We consider approximation by absolute distance, where an exact value x can be mapped to values in the range [x−t, x+t], for an approximation factor t, as well as approximation by separation, where values are mapped into t classes. We prove that in both cases the problem is in general NP-complete, but point to special cases that can be solved in polynomial time.

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