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Logic and precognizable sets of integers
 Bull. Belg. Math. Soc
, 1994
"... We survey the properties of sets of integers recognizable by automata when they are written in pary expansions. We focus on Cobham’s theorem which characterizes the sets recognizable in different bases p and on its generalization to N m due to Semenov. We detail the remarkable proof recently given ..."
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Cited by 92 (4 self)
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We survey the properties of sets of integers recognizable by automata when they are written in pary expansions. We focus on Cobham’s theorem which characterizes the sets recognizable in different bases p and on its generalization to N m due to Semenov. We detail the remarkable proof recently given by Muchnik for the theorem of CobhamSemenov, the original proof being published in Russian. 1
A Theory Of Justified Reformulations
, 1990
"... Present day systems, intelligent or otherwise, are limited by the conceptualizations of the world given to them by their designers. In this paper, we propose a novel, firstprinciples approach to performing incremental reformulations for computational efficiency. First, we define a reformulation to ..."
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Cited by 25 (0 self)
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Present day systems, intelligent or otherwise, are limited by the conceptualizations of the world given to them by their designers. In this paper, we propose a novel, firstprinciples approach to performing incremental reformulations for computational efficiency. First, we define a reformulation to be a shift in conceptualization: a change in the basic objects, functions, and relations assumed in a formulation. We then analyze the requirements for automating reformulation and show the need for justifying shifts in conceptualization. Inefficient formulations make irrelevant distinctions. A new class of metatheoretical justifications for a reformulation called irrelevance explanations, is presented. A logical irrelevance explanation demonstrates that certain distinctions made in the formulation are not necessary for the computation of a given class of problems. A computational irrelevance explanation shows that some distinctions are not useful with respect to a given problem solver fo...
On the Automata Size for Presburger Arithmetic
 In Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science (LICS 2004
, 2004
"... Automata provide an effective mechanization of decision procedures for Presburger arithmetic. However, only crude lower and upper bounds are known on the sizes of the automata produced by this approach. In this paper, we prove that the number of states of the minimal deterministic automaton for a Pr ..."
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Cited by 11 (1 self)
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Automata provide an effective mechanization of decision procedures for Presburger arithmetic. However, only crude lower and upper bounds are known on the sizes of the automata produced by this approach. In this paper, we prove that the number of states of the minimal deterministic automaton for a Presburger arithmetic formula is triple exponentially bounded in the length of the formula. This upper bound is established by comparing the automata for Presburger arithmetic formulas with the formulas produced by a quantifier elimination method. We also show that this triple exponential bound is tight (even for nondeterministic automata). Moreover, we provide optimal automata constructions for linear equations and inequations.
Defining new universes in manysorted logic
 A. Rényi Institute of Mathematics
, 2001
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The set of realizations of a maxplus linear sequence is semipolyhedral
 JOURNAL OF COMPUTER AND SYSTEM SCIENCES
, 2011
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manuscript No. (will be inserted by the editor) Proving SPARK Verification Conditions with SMT Solvers
"... Abstract We have constructed a tool for using SMT (SAT Modulo Theories) solvers to discharge verification conditions (VCs) from programs written in the SPARK language. The tool has API interfaces for some solvers and can drive any solver supporting the SMTLIB standard input language. SPARK is a sub ..."
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Abstract We have constructed a tool for using SMT (SAT Modulo Theories) solvers to discharge verification conditions (VCs) from programs written in the SPARK language. The tool has API interfaces for some solvers and can drive any solver supporting the SMTLIB standard input language. SPARK is a subset of Ada used primarily in highintegrity systems in the aerospace, defence, rail and security industries. Formal verification of SPARK programs is supported by tools produced by the UK company Altran Praxis. We report in this paper on our experience in proving SPARK VCs using the popular SMT solvers CVC3, Yices, Z3 and Simplify, and compare these solvers with Praxis’s automatic prover. We find that the SMT solvers can prove virtually all the VCs that are discharged by Praxis’s prover, and sometimes more. Average runtimes of the fastest SMT solvers are observed to be roughly 1 − 2 × that of the Praxis prover. Significant work is sometimes needed in translating VCs into a form suitable for input to the SMT solvers. A major contribution of the paper is a detailed presentation of the translations we implement. This is expected to be of interest to other users of SMT solvers.
Model Theory  A Palimpsest of Phil 516 by Scott Weinstein
, 1995
"... Introduction: 9/8 Definition 1 (Structure) Fill in the notion of a relational structure of a signature oe for a first order language. (Incomplete) Definition 2 (Signature) A signature of a structure A is specified by giving the set of constants of A and for each seperate n ! 0 the set of nary rela ..."
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Introduction: 9/8 Definition 1 (Structure) Fill in the notion of a relational structure of a signature oe for a first order language. (Incomplete) Definition 2 (Signature) A signature of a structure A is specified by giving the set of constants of A and for each seperate n ! 0 the set of nary relation symbols and the set of nary function symbols of A. Definition 3 (Class of structures K) The notion of a class of structures K being definable in a given logical language. (Incomplete) Definition 4 (Strict well ordering) A structure A is a strict well ordering iff A j= ' 8X ` jAj(X 6= ; ) 9y(y 2 X <F9.79