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Alternating TwoWay ACTree Automata
 IN PREPARATION
, 2002
"... We explore the notion of alternating twoway tree automata modulo the theory of finitely many associativecommutative (AC) symbols, some of them with a unit (AC1). This was prompted by questions arising in cryptographic protocol verification, where the emptiness question for intersections of such au ..."
Abstract

Cited by 11 (5 self)
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We explore the notion of alternating twoway tree automata modulo the theory of finitely many associativecommutative (AC) symbols, some of them with a unit (AC1). This was prompted by questions arising in cryptographic protocol verification, where the emptiness question for intersections of such automata is fundamental. We show that the use of conditional push clauses, or of alternation, leads to undecidability, already in the case of one AC or AC1 symbol, with only functions of arity zero. On the other hand, emptiness is decidable in the general case of many function symbols, including many AC or AC1 symbols, provided push clauses are unconditional and intersection clauses are final. To this end, extensive use of refinements of resolution is made.
Model Building with Ordered Resolution
 International Workshop on First Order Theorem Proving FTP'2000
, 2000
"... this paper, we propose to use clause sets to represent models. This idea is very simple and allows to combine in a well balanced way, expressive power with the \good" required properties of a reasonable model representation. Obviously, in order that the set of clauses specifying the model brings new ..."
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Cited by 4 (1 self)
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this paper, we propose to use clause sets to represent models. This idea is very simple and allows to combine in a well balanced way, expressive power with the \good" required properties of a reasonable model representation. Obviously, in order that the set of clauses specifying the model brings new information w.r.t. the initial one, a basic requirement is that these clause sets must have exactly one Herbrand model (on a given signature). Such clause sets are straightforward representations of their Herbrand models
Comparing Computational Representations of Herbrand Models
 Computational Logic and Proof Theory, 5th Kurt Godel Colloquium, KGC'97, volume 1289 of LNCS
, 1997
"... . Finding computationally valuable representations of models of predicate logic formulas is an important issue in the field of automated theorem proving, e.g. for automated model building or semantic resolution. In this article we treat the problem of representing single models independently of buil ..."
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Cited by 3 (2 self)
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. Finding computationally valuable representations of models of predicate logic formulas is an important issue in the field of automated theorem proving, e.g. for automated model building or semantic resolution. In this article we treat the problem of representing single models independently of building them and discuss the power of different mechanisms for this purpose. We start with investigating contextfree languages for representing single Herbrand models. We show their computational feasibility and prove their expressive power to be exactly the finite models. We show an equivalence with "ground atoms and ground equations" concluding equal expressive power. Finally we indicate how various other well known techniques could be used for representing essentially infinite models (i.e. models of not finitely controllable formulas), thus motivating our interest in relating model properties with syntactical properties of corresponding Herbrand models and in investigating connections betwe...
Combining inference and disinference rules with enumeration for model building (Extended Abstract)
, 1997
"... ) Ricardo Caferra and Nicolas Peltier Laboratory LEIBNIZIMAG 46, Avenue F'elix Viallet 38031 Grenoble Cedex FRANCE Ricardo.Caferra@imag.fr, Nicolas.Peltier@imag.fr Phone: (33) (0)4 76 57 46 59 1 Introduction The possibility of systematic model building in firstorder logic exists at least since t ..."
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Cited by 1 (1 self)
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) Ricardo Caferra and Nicolas Peltier Laboratory LEIBNIZIMAG 46, Avenue F'elix Viallet 38031 Grenoble Cedex FRANCE Ricardo.Caferra@imag.fr, Nicolas.Peltier@imag.fr Phone: (33) (0)4 76 57 46 59 1 Introduction The possibility of systematic model building in firstorder logic exists at least since the introduction of the tableaux method (Hintikka, Beth, Smullyan,: : : ), approximately 40 years ago. Some striking results in interactive model building have been obtained less than 20 years ago [21]. But it is only since less than 10 years that results on model building are regularly published [15, 7, 8, 5, 12, 13, 20, 22]. One important difference must be underlined between proof calculi and model building methods. Different calculi for firstorder logic (resolution, tableaux, connection method (matings), : : : ) are potentially able to prove the same class of theorems. In papers on model building methods what is emphasized in general is the class of models that the methods can (or cannot...