## On the compilability and expressive power of propositional planning formalisms (1998)

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### BibTeX

@TECHREPORT{Nebel98onthe,

author = {Bernhard Nebel},

title = {On the compilability and expressive power of propositional planning formalisms},

institution = {},

year = {1998}

}

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### Abstract

The recent approaches of extending the GRAPHPLAN algorithm to handle more expressive planning formalisms raise the question of what the formal meaning of “expressive power ” is. We formalize the intuition that expressive power is a measure of how concisely planning domains and plans can be expressed in a particular formalism by introducing the notion of “compilation schemes ” between planning formalisms. Using this notion, we analyze the expressiveness of a large family of propositional planning formalisms, ranging from basic STRIPS to a formalism with conditional effects, partial state specifications, and propositional formulae in the preconditions. One of the results is that conditional effects cannot be compiled away if plan size should grow only linearly but can be compiled away if we allow for polynomial growth of the resulting plans. This result confirms that the recently proposed extensions to the GRAPHPLAN algorithm concerning conditional effects are optimal with respect to the “compilability ” framework. Another result is that general propositional formulae cannot be compiled into conditional effects if the plan size should be preserved linearly. This implies that allowing general propositional formulae in preconditions and effect conditions adds another level of difficulty in generating a plan.

### Citations

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- 1994
(Show Context)
Citation Context ...ving the class does not increase the expressive power and should not affect the principal efficiency of 1. We assume that the reader has a basic knowledge of complexity theory (Garey & Johnson, 1979; =-=Papadimitriou, 1994-=-), and is familiar with the notion of polynomial many-one reductions and the complexity classes P, NP, coNP, and PSPACE. All other notions will be introduced in the paper when needed. 272COMPILABILIT... |

1805 |
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(Show Context)
Citation Context ...Kautz & Selman, 1996) are among the most efficient planning systems nowadays. However, it is generally felt that the planning formalism supported by these systems, namely, propositional basic STRIPS (=-=Fikes & Nilsson, 1971-=-), is not expressive enough. For this reason, much research effort (Anderson, Smith, & Weld, 1998; Gazen & Knoblock, 1997; Kambhampati, Parker, & Lambrecht, 1997; Koehler, Nebel, Hoffmann, & Dimopoulo... |

980 | Fast planning through planning graph analysis
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(Show Context)
Citation Context ... preserved linearly. This implies that allowing general propositional formulae in preconditions and effect conditions adds another level of difficulty in generating a plan. 1. Introduction GRAPHPLAN (=-=Blum & Furst, 1997-=-) and SATPLAN (Kautz & Selman, 1996) are among the most efficient planning systems nowadays. However, it is generally felt that the planning formalism supported by these systems, namely, propositional... |

532 | Pushing the envelope: Planning, propositional logic, and stochastic search
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(Show Context)
Citation Context ... that allowing general propositional formulae in preconditions and effect conditions adds another level of difficulty in generating a plan. 1. Introduction GRAPHPLAN (Blum & Furst, 1997) and SATPLAN (=-=Kautz & Selman, 1996-=-) are among the most efficient planning systems nowadays. However, it is generally felt that the planning formalism supported by these systems, namely, propositional basic STRIPS (Fikes & Nilsson, 197... |

297 | The computational complexity of propositional STRIPS planning - Bylander - 1994 |

295 |
ADL: Exploring the middle ground between STRIPS and the situation calculus
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(Show Context)
Citation Context ..., 1997; Kambhampati, Parker, & Lambrecht, 1997; Koehler, Nebel, Hoffmann, & Dimopoulos, 1997) has been devoted in extending GRAPHPLAN in order to handle more powerful planning formalisms such as ADL (=-=Pednault, 1989-=-). There appears to be a consensus on how much expressive power is added by a particular language feature. For example, everybody seems to agree that adding negative preconditions does not add very mu... |

261 | HTN planning: Complexity and expressivity - Erol, Hendler, et al. - 1994 |

239 | Some connections between nonuniform and uniform complexity classes - Karp, Lipton - 1980 |

221 |
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Citation Context ...definition, it follows almost immediately ACI that NC . Moreover, it has been shown that there are some languages in NC that are not in the non-uniform variant ACI of , which implies ACI ˜ ) that NC (=-=Furst, Saxe, & Sipser, 1984-=-). 5.5 Boolean Formulae Cannot be Compiled to Conditional Effects As we have seen in Section 5.3, Boolean formulae are quite expressive if they are used in combination with partial state specification... |

205 |
Computers and Intractability-A guide to the theory of NP-completeness
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Citation Context ...a formalism without leaving the class does not increase the expressive power and should not affect the principal efficiency of 1. We assume that the reader has a basic knowledge of complexity theory (=-=Garey & Johnson, 1979-=-; Papadimitriou, 1994), and is familiar with the notion of polynomial many-one reductions and the complexity classes P, NP, coNP, and PSPACE. All other notions will be introduced in the paper when nee... |

169 | Extending planning graphs to an adl subset
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(Show Context)
Citation Context ...l basic STRIPS (Fikes & Nilsson, 1971), is not expressive enough. For this reason, much research effort (Anderson, Smith, & Weld, 1998; Gazen & Knoblock, 1997; Kambhampati, Parker, & Lambrecht, 1997; =-=Koehler, Nebel, Hoffmann, & Dimopoulos, 1997-=-) has been devoted in extending GRAPHPLAN in order to handle more powerful planning formalisms such as ADL (Pednault, 1989). There appears to be a consensus on how much expressive power is added by a ... |

150 | Encoding plans in propositional logic
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(Show Context)
Citation Context ... our results give is that such a concise encoding will not be found by first translating conditional actions to unconditional actions and then using the “standard” encoding for unconditional actions (=-=Kautz, McAllester, & Selman, 1996-=-) to generate boolean formulae. However, addressing the problem of determining the conciseness of representation in this context appears to be an interesting and relevant topic for future research. Ac... |

148 | Complexity results for SAS+ planning - Bäckström, Nebel - 1995 |

129 | On the semantics of STRIPS - Lifschitz - 1986 |

123 | BLACKBOX: A new approach to the application of theorem proving to problem solving
- Kautz, Selman
(Show Context)
Citation Context ...nally, one may wonder how our results apply to planning approaches that are based on translating (bounded) planning problems to propositional logic such as SATPLAN (Kautz & Selman, 1996) or BLACKBOX (=-=Kautz & Selman, 1998-=-). Since the entire analysis of the relative expressiveness of planning formalisms uses the assumption that we compile from one planning formalism to another planning formalism, the results do not tel... |

116 | Encoding planning problems in non-monotonic logic programs - Dimopoulos, Nebel, et al. - 1997 |

97 | A survey on knowledge compilation
- Cadoli, Donini
- 1997
(Show Context)
Citation Context ...polynomial-time compilation scheme or we are able to prove that no compilation scheme exists. 6. This means that compilation schemes between planning formalisms are similar to knowledge compilations (=-=Cadoli & Donini, 1997-=-), where the fixed part of a computational problem is the domain structure and the variable part consists of the initial state and goal specifications. The main difference to the knowledge compilation... |

88 | Combining the expressiveness of UCPOP with the efficiency of Graphplan
- Gazen, Knoblock
(Show Context)
Citation Context ...nning formalism supported by these systems, namely, propositional basic STRIPS (Fikes & Nilsson, 1971), is not expressive enough. For this reason, much research effort (Anderson, Smith, & Weld, 1998; =-=Gazen & Knoblock, 1997-=-; Kambhampati, Parker, & Lambrecht, 1997; Koehler, Nebel, Hoffmann, & Dimopoulos, 1997) has been devoted in extending GRAPHPLAN in order to handle more powerful planning formalisms such as ADL (Pednau... |

69 | How to do things with worlds: On formalizing actions and plans - Brewka, Hertzberg - 1993 |

68 | Chee-Keng: Some consequences of non-uniform conditions on uniform classes - Yap - 1983 |

65 | Understanding and Extending Graphplan
- Kambhampati, Lambrecht, et al.
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(Show Context)
Citation Context ...d by these systems, namely, propositional basic STRIPS (Fikes & Nilsson, 1971), is not expressive enough. For this reason, much research effort (Anderson, Smith, & Weld, 1998; Gazen & Knoblock, 1997; =-=Kambhampati, Parker, & Lambrecht, 1997-=-; Koehler, Nebel, Hoffmann, & Dimopoulos, 1997) has been devoted in extending GRAPHPLAN in order to handle more powerful planning formalisms such as ADL (Pednault, 1989). There appears to be a consens... |

65 |
Turing machines that take advice
- Karp, Lipton
- 1982
(Show Context)
Citation Context ...elief that the polynomial hierarchy is proper, the above mentioned question of whether can be answered. It has been shown that would imply that the polynomial hierarchy collapses on the second level (=-=Karp & Lipton, 1982-=-), i.e., . This, however, is considered to be quite unlikely. Further, it has been shown that or fJe ygn i.e., , which again is considered to be very unlikely. We will use these result for proving tha... |

56 | The comparative linguistics of knowledge representation
- Gogic, Papadimitriou, et al.
- 1995
(Show Context)
Citation Context ...996; Erol, Hendler, & Nau, 1996; Gogic, Kautz, Papadimitriou, & Selman, 1995). Inspired by recent approaches to measure the expressiveness of knowledge representation formalisms (Cadoli et al., 1996; =-=Gogic et al., 1995-=-), we propose to address the questions of how expressive a planning formalism is by using the notion of compiling one planning formalism into another one. A compilation scheme from one planning formal... |

53 |
Complexity results for hierarchical task-network planning. To appear in Annals of Mathematics and Artijkial Intelligence Also available as
- Erol, Hendler, et al.
- 1994
(Show Context)
Citation Context ...polynomial-time computable, exponential-time computable, or even non-recursive. At least, this seems to be the idea when the notion of expressive power is discussed in similar contexts (Baader, 1990; =-=Erol et al., 1996-=-; Gogic et al., 1995; Cadoli et al., 1996). If we want to use such compilation schemes in practice, they should be reasonably efficient, of course. However, if we want to prove that one formalism is s... |

49 | Forming concepts for fast inference - Kautz, Selman - 1992 |

44 | Conditional effects in graphplan
- Anderson, Smith, et al.
- 1998
(Show Context)
Citation Context ... is generally felt that the planning formalism supported by these systems, namely, propositional basic STRIPS (Fikes & Nilsson, 1971), is not expressive enough. For this reason, much research effort (=-=Anderson, Smith, & Weld, 1998-=-; Gazen & Knoblock, 1997; Kambhampati, Parker, & Lambrecht, 1997; Koehler, Nebel, Hoffmann, & Dimopoulos, 1997) has been devoted in extending GRAPHPLAN in order to handle more powerful planning formal... |

35 | the polynomialtime hierarchy - Parity - 1984 |

30 | Expressive equivalence of planning formalisms
- Bäckström
- 1995
(Show Context)
Citation Context ... and the goal. While this restriction might sound unnecessarily restrictive, it turns out that existing practical approaches to compilation (Gazen & Knoblock, 1997) as well as theoretical approaches (=-=Bäckström, 1995-=-) consider only structured transformations where the operators can be transformed independently from the initial state and the goal description. From a technical point of view this restriction guarant... |

27 | Space efficiency of propositional knowledge representation formalisms
- Cadoli, Donini, et al.
- 2000
(Show Context)
Citation Context ...eratore, & Schaerf, 1996; Erol, Hendler, & Nau, 1996; Gogic, Kautz, Papadimitriou, & Selman, 1995). Inspired by recent approaches to measure the expressiveness of knowledge representation formalisms (=-=Cadoli et al., 1996-=-; Gogic et al., 1995), we propose to address the questions of how expressive a planning formalism is by using the notion of compiling one planning formalism into another one. A compilation scheme from... |

16 |
A Formal Definition for Expressive Power of Knowledge Representation Languages
- Baader
- 1990
(Show Context)
Citation Context ...as expressive as another one, but the mapping between the formalisms might not be computable at all. This, at least, seems to be the usual assumption made when the term expressive power is discussed (=-=Baader, 1990-=-; Cadoli, Donini, Liberatore, & Schaerf, 1996; Erol, Hendler, & Nau, 1996; Gogic, Kautz, Papadimitriou, & Selman, 1995). Inspired by recent approaches to measure the expressiveness of knowledge repres... |

10 | Comparing space efficiency of propositional knowledge representation formalisms
- Cadoli, Donini, et al.
(Show Context)
Citation Context ...as another one, but the mapping between the formalisms might not be computable at all. This, at least, seems to be the usual assumption made when the term expressive power is discussed (Baader, 1990; =-=Cadoli, Donini, Liberatore, & Schaerf, 1996-=-; Erol, Hendler, & Nau, 1996; Gogic, Kautz, Papadimitriou, & Selman, 1995). Inspired by recent approaches to measure the expressiveness of knowledge representation formalisms (Cadoli et al., 1996; Gog... |

4 | What is the expressive power of disjunctive preconditions
- Nebel
- 1999
(Show Context)
Citation Context ...etimes be easily compiled away. However, there are also cases when this is impossible. For example, it can be shown that CNF formulae cannot be compiled to basic STRIPS preserving plan size linearly (=-=Nebel, 1999),-=- which confirms Bäckström's (1995) conjecture that CNF-formulae in preconditions add to the expressive power of basic STRIPS. Another question is how reasonable our restrictions on a compilation sch... |

1 |
Complexity results for SAS+planning
- Bäckström, Nebel
- 1995
(Show Context)
Citation Context ...consider the existence problem in a particular planning formalism. Theorem 3X-PLANEX is PSPACE-complete for allXwithSvXvSBIC. 5. We do not consider planning formalisms identical to the SAS+formalism (=-=Bäckström & Nebel, 1995-=-), since we do not allow for multi-valued state variables. 279sNEBEL Proof. PSPACE-hardness ofS-PLANEX follows from a result by Bylander (1994, Corollary 3.2). Membership ofSBIC-PLANEX in PSPACE follo... |

1 |
Complexity results for SASÔ planning
- Bäckström, Nebel
- 1995
(Show Context)
Citation Context ...g formalism. Theorem 3 -PLANEX is PSPACE-complete for all with çŠóœõó§ç%íQëBì . 5. We do not consider planning formalisms identical to the SAS æ not allow for multi-valued state variables. formalism (=-=Bäckström & Nebel, 1995-=-), since we do 279NEBEL Proof. PSPACE-hardness of ç -PLANEX follows from a result by Bylander (1994, Corollary 3.2). Membership of ç%íQësì -PLANEX in PSPACE follows because we could, step by step, gu... |