Proceedings of the 13 ESSLLI Student Session - Multiple Choices ...

More documents

Recommendations

Info

Proceedings of the 13 th ESSLLI Student Session 6
Proceedings of the 13 th ESSLLI Student Session POP ∗ AND SEMANTIC LABELING USING SAT Martin Avanzini University of Innsbruck Abstract. The polynomial path order (POP ∗ for short) is a termination method that induces polynomial bounds on the innermost runtime complexity of term rewrite systems (TRSs). Semantic labeling is a transformation technique used for proving termination. In this paper we propose an efficient implementation of POP ∗ together with finite semantic labeling. This automation works by a reduction to the problem of boolean satisfiability. Satisfiability of the resulting formula is checked by a state-of-the-art SAT-solver. We have implemented the technique and experimental results confirm the feasibility of our approach. By semantic labeling, we significantly increase the power of POP ∗ . Term rewrite systems provide a conceptually simple but powerful abstract model of computation. In rewriting, proving termination is a long standing research field and consequently termination techniques applicable in an automated setting have been introduced quite early. Former research concentrated mainly on direct termination techniques (TeReSe, 2003). One such technique is the use of recursive path orders (RPOs), for instance the multiset path order (MPO) (Baader and Nipkow, 1998). Recently, the emphasis shifted toward transformation techniques like the dependency pair method (Arts and Giesl, 2000) or semantic labeling (Zantema, 1995). These methods significantly increase the possibility to automatically conclude termination. For direct termination techniques it is often possible to infer upper bounds on the derivational complexity of a rewrite system R from the termination proof. For instance, Hofbauer was the first to observe that termination via MPO implies the existence of a primitive recursive bound on the derivational complexity (Hofbauer, 1992). Here derivational complexity refers to the function that relates the length of the longest derivation sequence to the size of the initial term. It is thus quite natural to extend such a termination analysis of rewrite systems to the analysis of complexity properties. For the study of lower complexity bounds we recently introduced in (Avanzini and Moser, 2008) the polynomial path order (POP ∗ for short). This order is in essence a miniaturization of MPO, carefully crafted to induce polynomial bounds on the number of rewrite steps (c.f. Theorem 4). In this work, we show how to increase the power of POP ∗ by semantic labeling (Zantema, 1995). The idea behind semantic labeling is to label the function symbols of a rewrite system R with semantic information in such a way that direct termination methods become applicable for the labeled rewrite system Rlab. In order to label R, one needs to define suitable interpretation- and labeling-functions for all symbols appearing in R. Naturally, these functions have to be chosen such that POP ∗ is applicable to the labeled system. To find them automatically, we extend the propositional encoding from (Avanzini and Moser, 2008). Satisfiability of the constructed formula certifies the existence of a labeled system Rlab that is compatible with POP ∗ . Finite semantic labeling is non-termination preserving and moreover, it is complexity preserving. Thus from compatibility of Rlab with POP ∗ we conclude that R admits a polynomial runtime complexity (c.f. Lemma 6). 7
Page 1 and 2: Proceedings of the 13 th ESSLLI Stu
Page 3 and 4: Contents Preface . . . . . . . . .
Page 5: Preface Proceedings of the 13 th ES
Page 9 and 10: mechanism of the encoded function.
Page 13 and 14: The table below presents experiment
Page 17 and 18: SIMULATING SPOKEN DIALOGUE WITH A F
Page 19 and 20: 21 Speech Generation Speech generat
Page 31 and 32: We now state our update semantics f
Page 33 and 34: 3 Comparison With a Partition Seman
Page 35 and 36: We take this objection seriously, a
Page 37 and 38: BARE PREDICATION AND KINDS ∗ Bert
Page 39 and 40: The reason why the b-variants are o
Page 41 and 42: 2006)). The second is that nouns re
Page 43 and 44: 43 Non-bare predication and non-uni
Page 45 and 46: References Proceedings of the 13 th
Page 47 and 48: DIAGRAMMATIC REASONING WITH ENHANCE
Page 51 and 52: previously. Proceedings of the 13 t
Page 53 and 54: type theory of Euler diagrams based
Page 55 and 56: software (Stapleton and Delaney, 20
Page 57 and 58:
FICTIONAL CONTINGENCIES Gemma Celes
Page 59 and 60:
Proceedings of the 13 th ESSLLI Stu
Page 61 and 62:
Page 63 and 64:
of as the individuals that these fi
Page 65 and 66:
Page 67 and 68:
Page 69 and 70:
Page 71 and 72:
Page 73 and 74:
Page 75 and 76:
TOWARDS A NEW CHARACTERISATION OF C
Page 77 and 78:
The following paper continues this
Page 79 and 80:
Page 81 and 82:
only one increasing chain completel
Page 83 and 84:
the minimal step width seems to be
Page 85 and 86:
Page 87 and 88:
etrieved in order to check it again
Page 89 and 90:
Results The percentages of correct
Page 91 and 92:
The complexity of relative clauses
Page 93 and 94:
References Proceedings of the 13 th
Page 95 and 96:
A SALIENCE-DRIVEN APPROACH TO SPEEC
Page 97 and 98:
Page 99 and 100:
2. the linguistic salience or “re
Page 101 and 102:
Page 103 and 104:
where the expectations provided by
Page 105 and 106:
A LOGIC WITH A CONDITIONAL PROBABIL
Page 107 and 108:
• v : F orC × W −→ {0, 1} is
Page 109 and 110:
Page 111 and 112:
Lemma 4 M ∗ is a measurable model
Page 113 and 114:
is a tautology. Now we can equivale
Page 115 and 116:
A PROOF-THEORETIC APPROACH TO FRENC
Page 117 and 118:
Page 119 and 120:
Page 121 and 122:
Page 123 and 124:
References Abeillé, A., Godard, D.
Page 125 and 126:
INFINITE GAMES FROM AN INTUITIONIST
Page 127 and 128:
Page 129 and 130:
Page 131 and 132:
Page 133 and 134:
6 Further problems Proceedings of t
Page 135 and 136:
Page 137 and 138:
pointers to the text, containing th
Page 139 and 140:
example in a comparatively short te
Page 141 and 142:
Such an example is: Constant modifi
Page 143 and 144:
WORD SPACE MODELS OF SEMANTIC SIMIL
Page 145 and 146:
tween semantic similarity and seman
Page 147 and 148:
wu & palmer 0.0 0.2 0.4 0.6 0.8 1.0
Page 149 and 150:
Page 151 and 152:
frequency F−score 0 100 200 300 4
Page 153 and 154:
EXAMINING THE NOTICING FUNCTION OF
Page 155 and 156:
Page 157 and 158:
effects of input flood and individu
Page 159 and 160:
Page 161 and 162:
Page 163 and 164:
Page 165 and 166:
CDIPROVER3: A TOOL FOR PROVING DERI
Page 167 and 168:
Page 169 and 170:
Example 8. Consider the TRS given i
Page 171 and 172:
Page 173 and 174:
Page 175 and 176:
THE RANK(S) OF A TOTALLY LEXICALIST
Page 177 and 178:
Page 179 and 180:
Page 181 and 182:
Page 183 and 184:
Page 185 and 186:
EXPRESSING CONJUNCTIVE AND AGGREGAT
Page 187 and 188:
Page 189 and 190:
(Rule) (Semantic Action) Qwh → In
Page 191 and 192:
(⇐) We will prove, by induction o
Page 193 and 194:
Page 195 and 196:
1 Introduction INTERROGATION IN DYN
Page 197 and 198:
Page 199 and 200:
to hold for questions to be felicit
Page 201 and 202:
5 Further research One goal for a s
Page 203 and 204:
THE SEMANTIC CHANGE OF THE FRENCH -
Page 205 and 206:
Page 207 and 208:
Page 209 and 210:
Page 211 and 212:
6 Conclusion In this paper, I inves
Page 213 and 214:
ADVERSARY IMPLICATURES ∗ Grégoir
Page 215 and 216:
Page 217 and 218:
Page 219 and 220:
2.2.1 The derivation of Q-Implicatu
Page 221 and 222:
of the first, the relation of Contr
Page 223 and 224:
List of authors Martin Avanzini Mar
show all

Proceedings of the 13 ESSLLI Student Session - Multiple Choices ...

Create successful ePaper yourself

Delete template?

Save as template?