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{{Short description|Temporal logic}}
'''Property Specification Language''' ('''PSL''') is a [[temporal logic]] extending [[linear temporal logic]] with a range of operators for both ease of expression and enhancement of expressive power. PSL makes an extensive use of [[regular expressions]] and syntactic sugaring. It is widely used in the hardware design and verification industry, where [[formal verification]] tools (such as [[model checking]]) and/or [[logic simulation]] tools are used to prove or refute that a given PSL formula holds on a given design.
PSL was initially developed by [[Accellera]] for specifying [[Property (philosophy)|properties]] or [[assertion (computing)|assertions]] about hardware designs. Since September 2004 the [[standardization|standard]]ization on the language has been done in [[IEEE]] 1850 working group. In September 2005, the IEEE 1850 Standard for Property Specification Language (PSL) was announced.
== Syntax and semantics ==
PSL can express that if some scenario happens now, then another scenario should happen some time later. For instance, the property "a {{mono|request}} should always eventually be {{mono|grant}}ed" can be expressed by the PSL formula:
<syntaxhighlight lang="text"> always (request -> eventually! grant)
</syntaxhighlight>
The property "every {{mono|request}} that is immediately followed by an {{mono|ack}} signal, should be followed by a complete {{mono|data transfer}}, where a complete data transfer is a sequence starting with signal {{mono|start}}, ending with signal {{mono|end}} in which {{mono|busy}} holds at the meantime" can be expressed by the PSL formula:
<syntaxhighlight lang="text"> (true[*]; req; ack) |=> (start; busy[*]; end) </syntaxhighlight>
A trace satisfying this formula is given in the figure on the right.
[[File:The trigger operator - slide 1.jpg|thumb|a simple trace satisfying <syntaxhighlight lang="text">(true[*]; req; ack) |=> (start; busy[*]; end)</syntaxhighlight>]]
PSL's temporal operators can be roughly classified into ''LTL-style'' operators and ''regular-expression-style'' operators. Many PSL operators come in two versions, a strong version, indicated by an exclamation mark suffix ( {{mono|!}} ), and a weak version. The ''strong version'' makes eventuality requirements (i.e. require that something will hold in the future), while the ''weak version'' does not. An ''underscore suffix'' ( {{mono|_}} ) is used to differentiate ''inclusive'' vs. ''non-inclusive'' requirements. The {{mono|_a}} and {{mono|_e}} suffixes are used to denote ''universal'' (all) vs. ''existential'' (exists) requirements. Exact time windows are denoted by {{mono|[n]}} and flexible by {{mono|[m..n]}}.
=== SERE-style operators===
The most commonly used PSL operator is the "suffix-implication" operator (also known as the "triggers" operator), which is denoted by {{mono|{{!}}{{=}}>}}. Its left operand is a PSL regular expression and its right operand is any PSL formula (be it in LTL style or regular expression style). The semantics of {{mono|r {{!}}{{=}}> p}} is that on every time point i such that the sequence of time points up to i constitute a match to the regular expression r, the path from i+1 should satisfy the property p. This is exemplified in the figures on the right.
[[File:The trigger operator - slide 2.jpg|thumb|path satisfying ''r triggers p'' in two non-overlapping ways]]
[[File:The trigger operator - slide 3.jpg|thumb|path satisfying ''r triggers p'' in two overlapping ways]]
[[File:The trigger operator - slide 4.jpg|thumb|path satisfying ''r triggers p'' in three ways]]
The regular expressions of PSL have the common operators for concatenation ({{mono|;}}), Kleene-closure ({{mono|*}}), and union ({{mono|{{!}}}}), as well as operator for fusion ({{mono|:}}), intersection ({{mono|&&}}) and a weaker version ({{mono|&}}), and many variations for consecutive counting {{mono|[*n]}} and in-consecutive counting e.g. {{mono|[{{=}}n]}} and {{mono|[->n]}}.
The trigger operator comes in several variations, shown in the table below.
Here {{
{| class="wikitable"
| <
| if there is a match of s, then there is a match of t on the suffix of the trace,
*t starts the cycle after s ends,
*the match of t must reach to its end
|-
| <
| if there is a match of s, then there is a match of t on the suffix of the trace,
*t starts the same cycle that s ends,
*the match of t must reach to its end
|-
| <
| if there is a match of s, then there is a match of t on the suffix of the trace,
*t starts the cycle after s ends,
*the match of t may "get stuck" in the middle
|-
| <
| if there is a match of s, then there is a match of t on the suffix of the trace,
*t starts the same cycle that s ends,
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Operators for concatenation, fusion, union, intersection and their variations are shown in the table below.
Here {{
{| class="wikitable"
| <code> s ; t </code>
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| match of s followed by a match of t, t starts the same cycle that s ends
|-
| <
| match of s or match of t
|-
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|-
| <code> s within t </code>
| match of s within a match of t, abbreviation of ([*]; s; [*]) &&
|-
|}
Operators for consecutive repetitions are shown in the table below.
Here {{
{| class="wikitable"
| <code> s[*i] </code>
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|}
Operators for non-consecutive repetitions are shown in the table below.
Here {{
{| class="wikitable"
| <code> b[=i] </code>
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*equivalent to (!b[*];b)[*i]; !b[*]
|-
| <
| at least i and
*equivalent to (!b[*];b)[*i..j]; !b[*]
|-
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*equivalent to (!b[*];b)[*i..]; !b[*]
|-
| <
| m not necessarily consecutive repetitions of b ending with b,
*equivalent to (!b[*];b)[*m]
|-
| <code> b[->m:n] </code>
| at least m and
*equivalent to (!b[*];b)[*m..n]
|-
| <code> b[->m..] </code>
| at least m not necessarily consecutive repetitions of b ending with b,
*equivalent to (!b[*];b)[*
|-
| <code> b[->] </code>
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|}
Below is a sample of some LTL-style operators of PSL.
Here {{mono|p}} and {{mono|q}} are any PSL formulas.
{| class="wikitable"
| {{code|always p}}
| property p holds on every time point
|-
| {{code|never p}}
| property p does not hold on any time point
|-
| {{code|eventually! p}}
| there exists a future time point where p holds
|-
| {{code|next! p}}
| there exists a next time point, and p holds on this point
|-
| {{code|next p}}
| if there exists a next time point, then p holds on this point
|-
| {{code|next![n] p}}
| there exists an n-th time point, and p holds on this point
|-
| {{code|next[n] p}}
| if there exists an n-th time point, then p holds on this point
|-
| {{code|next_e![m..n] p}}
| there exists a time point, within m-th to n-th from the current where p holds.
|-
| {{code|next_e[m..n] p}}
| if there exists at least n-th time points, then p holds on one of the m-th to n-th points.
|-
| {{code|next_a![m..n] p}}
| there exists at least n more time points and p holds in all the time points between the m-th to the n-th, inclusive.
|-
| {{code|next_a[m..n] p}}
| p holds on all the next m-th through n-th time points, however many exist
|-
| {{code|p until! q}}
| there exists a time point where q holds, and p hold up until that time point
|-
| {{code|p until q}}
| p holds up until a time point where q hold, if such exists
|-
| {{code|p until!_ q}}
| there exists a time point where q holds, and p holds up until that time point and in that time point
|-
| {{code|p until_ q}}
| p holds up until a time point where q holds, and in that time point, if such exists
|-
| {{code|p before! q}}
| p holds strictly before the time point where q holds, and p eventually holds
|-
| {{code|p before q}}
| p holds strictly before the time point where q holds, if p never holds, then neither does q
|-
| {{code|p before!_ q}}
| p holds before or at the same time point where q holds, and p eventually holds
|-
| {{code|p before_ q}}
| p holds before or at the same time point where q holds, if p never holds, then neither does q
|-
|}
=== Sampling operator===
Sometimes it is desirable to change the definition of the ''next time-point'', for instance in multiply-clocked designs, or when a higher level of abstraction is desired. The ''sampling operator'' (also known as the ''clock operator''), denoted {{mono|@}}, is used for this purpose. The formula {{mono| p @ c }} where {{mono| p}} is a PSL formula and {{mono|c}} a PSL Boolean expressions holds on a given path if {{mono| p}} on that path projected on the cycles in which {{mono| c}} holds, as exemplified in the figures to the right.
[[File:Need for multiple clocks.jpg|thumb|path and formula showing need for a sampling operator]]
The first property states that "every {{mono|request}} that is immediately followed by an {{mono|ack}} signal, should be followed by a complete {{mono|data transfer}}, where a complete data transfer is a sequence starting with signal {{mono|start}}, ending with signal {{mono|end}} in which {{mono|data}} should hold at least 8 times:
<syntaxhighlight lang="text"> (true[*]; req; ack) |=> (start; data[=8]; end) </syntaxhighlight>
But sometimes it is desired to consider only the cases where the above signals occur on a cycle where {{mono|clk}} is high.
This is depicted in the second figure in which although the formula
<syntaxhighlight lang="text"> ((true[*]; req; ack) |=> (start; data[*3]; end)) @ clk </syntaxhighlight>
uses {{mono|data[*3]}} and {{mono|[*n]}} is consecutive repetition, the matching trace has 3 non-consecutive time points where {{mono|data}} holds, but when considering only the time points where {{mono|clk}} holds, the time points where {{mono|data}} hold become consecutive.
[[File:Multiple clocks.jpg|thumb|path and formula showing effect of the sampling operator @]]
The semantics of formulas with nested @ is a little subtle. The interested reader is referred to [2].
=== Abort operators ===
PSL has several operators to deal with truncated paths (finite paths that may correspond to a prefix of the computation). Truncated paths occur in bounded-model checking, due to resets and in many other scenarios. The abort operators, specify how eventualities should be dealt with when a path has been truncated. They rely on the truncated semantics proposed in [1].
Here {{
{| class="wikitable"
| <code> p async_abort b </code>
| either p holds or p does not fail up until b holds
* b recognized asynchronously
|-
| <code> p sync_abort b </code>
| either p holds or p does not fail up until
* b recognized synchronously
|-
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|}
===Expressive power===
PSL subsumes the temporal logic [[Linear temporal logic|LTL]] and extends its expressive power to that of the [[omega-regular languages]]. The augmentation in expressive power, compared to that of LTL, which has the expressive power of the star-free ω-regular expressions, can be attributed to the ''suffix implication'', also known as the ''triggers'' operator, denoted "|->". The formula ''r |-> f'' where ''r'' is a regular expression and ''f'' is a temporal logic formula holds on a computation ''w'' if any prefix of ''w'' matching ''r'' has a continuation satisfying ''f''. Other non-LTL operators of PSL are the ''@'' operator, for specifying multiply-clocked designs, the ''abort'' operators, for dealing with hardware resets, and ''local variables'' for succinctness.
===Layers===
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===Language compatibility===
Property Specification Language can be used with multiple electronic system design languages (HDLs) such as:
* [[VHDL]] (IEEE 1076)
* [[Verilog]] (IEEE 1364)
* [[SystemVerilog]] (IEEE 1800)
* [[SystemC]] (IEEE 1666) by [[Open SystemC Initiative|Open SystemC Initiative (OSCI)]].
When PSL is used in conjunction with one of the above HDLs, its Boolean layer uses the operators of the respective HDL.
==References==
*{{
**IEC 62531:2007 {{
*{{
**IEC 62531:2012 {{
*{{cite book|doi=10.1007/978-3-540-45069-6_3|chapter=Reasoning with Temporal Logic on Truncated Paths|title=[[Computer Aided Verification]]|volume=2725|pages=27|series=Lecture Notes in Computer Science|year=2003|last1=Eisner|first1=Cindy|last2=Fisman|first2=Dana|author2-link=Dana Fisman|last3=Havlicek|first3=John|last4=Lustig|first4=Yoad|last5=McIsaac|first5=Anthony|last6=Van Campenhout|first6=David|isbn=978-3-540-40524-5|chapter-url=http://www.research.ibm.com/people/e/eisner/papers/cav49.pdf}}
*{{cite book|doi=10.1007/3-540-45061-0_67|chapter=The Definition of a Temporal Clock Operator|title=Automata, Languages and Programming|volume=2719|pages=857|series=Lecture Notes in Computer Science|year=2003|last1=Eisner|first1=Cindy|last2=Fisman|first2=Dana|author2-link=Dana Fisman|last3=Havlicek|first3=John|last4=McIsaac|first4=Anthony|last5=Van Campenhout|first5=David|isbn=978-3-540-40493-4|chapter-url=http://www.cis.upenn.edu/~fisman/documents/EFHMV_ICALP03_full.pdf}}
==External links==
* [http://www.eda.org/ieee-1850 IEEE 1850 working group]
* [https://web.archive.org/web/20051210035642/http://standards.ieee.org/announcements/pr_1850psl.html IEEE Announcement September 2005]
* [http://www.accellera.org/ Accellera]
* [http://www.project-veripage.com/psl_tutorial_1.php Property Specification Language Tutorial]
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===Books on PSL===
* [http://www.systemverilog.us/psl_info.html Using PSL/Sugar for Formal and Dynamic Verification 2nd Edition, Ben Cohen, Ajeetha Kumari, Srinivasan Venkataramanan]
* [
{{Programmable Logic}}
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[[Category:Formal specification languages]]
[[Category:IEEE DASC standards]]
[[Category:IEC standards
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